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1quiver.jpg (Wed Oct 21 22:08:22 2009)

16061983.pdf (Mon Apr 29 14:23:24 2013) Linked to by: Kan complex

1dAdinkraExample.png (Mon Feb 13 13:37:24 2017)

2quiver.jpg (Wed Oct 21 22:05:24 2009)

2Cell.jpg (Wed Nov 9 09:00:23 2016)

2bundrecon.pdf (Thu Jan 15 11:59:54 2009) Linked to by: generalized universal bundle

2horns.jpg (Thu Feb 18 07:11:14 2016)

3Cell.jpg (Wed Nov 9 09:12:31 2016)

3dSubgroupsOfG2.jpg (Wed Jan 20 12:24:14 2016)

3simplex_facemaps.jpg (Fri Oct 9 06:10:04 2009)

3simplex_in_3cube.jpg (Fri Oct 9 05:37:14 2009)

ACTOIT.pdf (Fri Mar 8 16:16:07 2013) Linked to by: persistent homology

ADE2Cycle.jpeg (Tue Aug 11 06:05:34 2015)

AHomotopy.jpg (Tue Apr 12 13:49:53 2016)

AMSFallSlides.pdf (Wed Dec 17 01:54:42 2014)

AMSFallSlides.pdf (Tue Dec 16 22:28:01 2014)

AMSFallnotes.pdf (Tue Dec 16 22:27:13 2014)

AbstractHomotopy.pdf (Fri Feb 12 14:31:17 2010) Linked to by: cylinder functor

AdamsHopfInvariantProofFlow.jpg (Fri Jan 22 13:26:41 2016)

AdinkraRule.png (Mon Feb 13 09:07:44 2017)

AdinkrasFrom4d.png (Mon Feb 13 14:05:06 2017)

AdinkrasFromCode.png (Mon Feb 13 13:41:22 2017)

AjunctionsForSuperCohesion.png (Tue Nov 29 10:42:03 2016)

AlexHellerbibtex.bib (Mon Nov 12 11:33:43 2012) Linked to by: Alex Heller

AlexHellerpub.pdf (Mon Nov 12 11:33:17 2012) Linked to by: Alex Heller

AlexHeller.pdf (Mon Oct 29 23:58:22 2012) Linked to by: Alex Heller

AlgKan.pdf (Tue Mar 2 21:07:05 2010)

AlgKanB.pdf (Tue Mar 2 22:25:16 2010)

AlgKanC.pdf (Tue Mar 2 23:00:42 2010)

AlgMod.pdf (Tue Mar 2 23:03:46 2010)

AlgModB.pdf (Wed Mar 3 09:41:21 2010) Linked to by: Thomas Nikolaus

AlgModC.pdf (Wed Mar 3 10:22:56 2010)

AndersonVariationalBicomplex.pdf (Thu Sep 1 05:22:30 2016) Linked to by: variational calculus, jet bundle, variational bicomplex, EulerLagrange complex, Helmholtz operator

AndrewStacey.png (Wed Sep 30 10:01:44 2009)

AramianANSS.pdf (Fri Jan 29 15:12:21 2016) Linked to by: Adams resolution, Adams spectral sequence

Arone95.pdf (Sun Feb 9 04:42:58 2014) Linked to by: Goodwillie calculus

Asada.pdf (Mon Mar 15 21:14:12 2010) Linked to by: string structure

AssociativityDiagram.png (Tue Jan 24 15:07:52 2017)

AtiyahKReal.pdf (Wed Apr 16 05:43:58 2014) Linked to by: KR cohomology theory

AttachingSpace.jpg (Tue Apr 5 09:20:47 2016)

AufhebungAnnouncement.pdf (Thu Nov 12 13:23:39 2015)

AufhebungConcert.pdf (Thu Nov 12 13:13:11 2015)

AufhebungDetail.jpg (Thu Nov 12 13:12:39 2015)

AwodeyBirkedalLocalTopos.pdf (Thu Nov 17 10:10:00 2011) Linked to by: local geometric morphism, modal type theory

BBSEquilogical.pdf (Tue Mar 4 05:19:06 2014) Linked to by: equilogical space

BPSLinear.pdf (Tue Feb 4 01:03:05 2014) Linked to by: !modality

BakalovKirillovChapter5.pdf (Mon Sep 15 21:09:21 2014) Linked to by: mapping class group, modular functor

BattenfeldDomains.pdf (Mon Mar 3 02:36:50 2014) Linked to by: computable function (analysis), function realizability

BauerLumsdaineUnivalence.pdf (Thu Nov 24 17:06:07 2011) Linked to by: Oberwolfach Ho TTCoq tutorial

BehrensANSSfortmf.pdf (Thu Feb 4 10:06:13 2016) Linked to by: Adams spectral sequence

BelmansDuality.pdf (Fri Jul 4 03:59:49 2014) Linked to by: Grothendieck duality, FourierMukai transform

BenZviGeometricFunctionTheory.pdf (Thu Jan 8 16:37:12 2009) Linked to by: David BenZvi, geometric function theory

BenZviHamburg2009.pdf (Mon Feb 23 09:46:19 2009) Linked to by: David BenZvi

BentonLinearLogic.pdf (Wed Jan 29 03:10:57 2014) Linked to by: dependent linear type theory

BerkovichAnalyticSpaces.pdf (Mon Jan 2 17:23:41 2012)

BernsteinDModule.pdf (Sat Feb 15 14:29:30 2014) Linked to by: six operations, holonomic Dmodule, Dmodule

BhattPerfectoidSpace.pdf (Tue Sep 16 07:31:22 2014) Linked to by: perfectoid space

BlakeSpinC.pdf (Wed Nov 7 02:16:12 2012) Linked to by: spin^c structure

BlauGeometricQuantization.pdf (Thu Sep 27 18:34:11 2012) Linked to by: polarization, quantum observable, geometric quantization

BlochTamagawa.pdf (Tue Aug 26 20:40:12 2014) Linked to by: Tamagawa number, Birch and SwinnertonDyer conjecture

BonnLogo.png (Wed Feb 3 04:41:21 2016)

BonoraSuperGS.pdf (Fri Mar 11 22:24:37 2011) Linked to by: GreenSchwarz mechanism, heterotic string theory

BradyTrimbleString.pdf (Sat Feb 8 16:44:16 2014) Linked to by: A string diagram calculus for predicate logic

BraidDiagramForHomologyOnTripled.jpg (Tue Apr 12 04:25:44 2016)

BraneSolutionsInSupergravity.jpg (Wed Dec 9 12:54:52 2015)

BrownAbstractHomotopyTheory.pdf (Wed Jan 14 10:55:37 2009) Linked to by: homotopical cohomology theory, Brown AHT, category of fibrant objects

Brylinski94.pdf (Fri Jun 27 22:37:54 2014) Linked to by: universal ChernSimons line 3bundle, higher regulator, exponential exact sequence, divisor (algebraic geometry), holomorphic line 2bundle

BumpSpectralTheory.pdf (Fri Aug 22 01:50:28 2014) Linked to by: Selberg zeta function, Selberg trace formula, zeta function of a Riemann surface

ButterfieldNoether.pdf (Wed May 22 02:49:54 2013) Linked to by: Noether's theorem

BuzzardForms.pdf (Wed Jul 2 00:48:52 2014) Linked to by: form of an algebraic group

BuzzardReductive.pdf (Thu Jun 19 20:36:24 2014) Linked to by: reductive algebraic group

Cactus_ABC_Big.jpg (Wed Sep 16 21:42:20 2009)

Cactus_A_Big.jpg (Wed Sep 16 21:40:56 2009)

Cactus_Graph_Df_eq_llPcdPrlQcdQrcPQr.jpg (Sat Sep 19 13:02:42 2009)

Cactus_Graph_DfaPQ_eq_lldPrldQrr.jpg (Sat Sep 19 13:38:45 2009)

Cactus_Graph_DfaPlQr_eq_ldPrdQ.jpg (Sat Sep 19 14:14:21 2009)

Cactus_Graph_DfalPrQ_eq_dPldQr.jpg (Sat Sep 19 14:21:05 2009)

Cactus_Graph_DfalPrlQr_eq_dP_dQ.jpg (Sat Sep 19 14:24:23 2009)

Cactus_Graph_Ef_eq_lPcdPrlQcdQr.jpg (Sat Sep 19 13:00:20 2009)

Cactus_Graph_EfaPQ_eq_ldPrldQr.jpg (Sat Sep 19 15:24:23 2009)

Cactus_Graph_EfaPlQr_eq_ldPrdQ.jpg (Sat Sep 19 15:26:55 2009)

Cactus_Graph_EfalPrQ_eq_dPldQr.jpg (Sat Sep 19 15:30:17 2009)

Cactus_Graph_EfalPrlQr_eq_dP_dQ.jpg (Sat Sep 19 15:32:22 2009)

Cactus_Graph_Existential_P_And_Q.jpg (Fri Sep 18 15:17:04 2009)

Cactus_Graph_F_Equals_P_And_Q.jpg (Sat Sep 19 04:12:56 2009)

Cactus_Graph_Lobe_Connective.jpg (Fri Sep 18 15:00:22 2009)

Cactus_Graph_Lobe_Rule.jpg (Sat Sep 19 14:26:50 2009)

Cactus_Graph_Node_Connective.jpg (Fri Sep 18 15:02:14 2009)

Cactus_Graph_PQ_Diff_lldPrldQrr.jpg (Fri Sep 18 16:36:19 2009)

Cactus_Graph_PQ_Difference_Conj_At_Conj.jpg (Sat Sep 19 13:08:18 2009)

Cactus_Graph_Spike_Rule.jpg (Sat Sep 19 14:29:05 2009)

Cactus_Graph_lPcdPr.jpg (Fri Sep 18 15:30:16 2009)

Cactus_Graph_lPcdPrlQcdQr.jpg (Fri Sep 18 15:25:08 2009)

Cactus_Graph_llPcdPrlQcdQrcPQr.jpg (Fri Sep 18 15:36:22 2009)

Cactus_Graph_ll_cdPrl_cdQrc_r.jpg (Fri Sep 18 15:48:27 2009)

Cactus_Graph_lldPrldQrr.jpg (Fri Sep 18 15:50:22 2009)

Cactus_lAcBcCr_Big.jpg (Thu Sep 17 14:32:56 2009)

Cactus_lAcBr_Big.jpg (Thu Sep 17 12:44:45 2009)

Cactus_lAclBcCrr_Big.jpg (Thu Sep 17 16:35:17 2009)

Cactus_lAlBrr_Big.jpg (Thu Sep 17 12:43:08 2009)

Cactus_lAr_Big.jpg (Thu Sep 17 01:20:15 2009)

Cactus_lXclArclBrclCrr_Big.jpg (Thu Sep 17 17:00:28 2009)

Cactus_llAcBrr_Big.jpg (Thu Sep 17 14:31:01 2009)

Cactus_llArclBrclCrr_Big.jpg (Thu Sep 17 14:35:02 2009)

Cactus_llArlBrlCrr (Thu Sep 17 01:22:46 2009)

Cactus_llArlBrlCrr_Big (Thu Sep 17 01:36:21 2009)

Cactus_llArlBrlCrr_Big.jpg (Thu Sep 17 01:42:30 2009)

CamaraOnArakelov11.pdf (Tue May 27 13:24:49 2014) Linked to by: Arakelov geometry

CarrellZariskiTopology.pdf (Mon Apr 24 03:47:50 2017) Linked to by: Zariski topology

ChartsOfAManifold.png (Tue Feb 7 13:24:39 2017)

ChernConnections.pdf (Thu Sep 11 19:26:33 2014) Linked to by: Chern connection

ClassicalAdamsSpectralSequence.jpg (Mon Mar 14 15:40:28 2016)

ClosedAndOpenSubsets.png (Wed Apr 5 14:57:43 2017)

ClosedIntervalQuotientedToCircle.pdf (Fri Apr 14 11:05:12 2017)

Coh_fig_1.gif (Sat Sep 3 23:03:00 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_10.gif (Sat Sep 3 23:09:34 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_11.gif (Sat Sep 3 23:10:19 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_12.gif (Sat Sep 3 23:10:57 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_13.gif (Sat Sep 3 23:11:38 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_14.gif (Sat Sep 3 23:12:22 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_15.gif (Sat Sep 3 23:13:18 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_16.gif (Sat Sep 3 23:14:24 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_17.gif (Sat Sep 3 23:15:06 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_18.gif (Sat Sep 3 23:16:01 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_19.gif (Sat Sep 3 23:16:58 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_2.gif (Sat Sep 3 23:03:43 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_20.gif (Sat Sep 3 23:17:38 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_3.gif (Sat Sep 3 23:04:25 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_4.gif (Sat Sep 3 23:05:02 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_5.gif (Sat Sep 3 23:05:48 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_6.gif (Sat Sep 3 23:06:43 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_7.gif (Sat Sep 3 23:07:27 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_8.gif (Sat Sep 3 23:08:09 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Coh_fig_9.gif (Sat Sep 3 23:08:54 2011) Linked to by: Mac Lane's proof of the coherence theorem for monoidal categories

Completion.pdf (Fri Aug 15 02:40:28 2014) Linked to by: adic residual

ComputationWithYoungTableaux.jpg (Tue Jan 10 18:02:07 2017)

Con_not_WISC.pdf (Thu Nov 8 05:01:32 2012)

ConstableTriumphOfTypes.pdf (Mon Jan 13 03:35:25 2014) Linked to by: type theory, computational type theory, Nu PRL

CorfieldVortexAtoms.pdf (Thu Sep 18 19:58:31 2014) Linked to by: On Vortex Atoms

CurienGarnerHofmann.pdf (Wed May 7 02:26:23 2014) Linked to by: substitution, categorical model of dependent types, relation between type theory and category theory

DBZLecture1.ps (Tue May 19 13:12:02 2009) Linked to by: Northwestern TFT Conference 2009

DBZLecture2.ps (Wed May 20 13:13:00 2009) Linked to by: Northwestern TFT Conference 2009

DBZLecture3.ps (Thu May 21 04:50:19 2009) Linked to by: Northwestern TFT Conference 2009

DBZLecture4.ps (Fri May 22 17:10:33 2009) Linked to by: Northwestern TFT Conference 2009

DRobertsUniversalSimpBunds.pdf (Wed Jul 21 13:03:29 2010)

DSSFusionSlides.pdf (Sun Jul 10 13:43:25 2011) Linked to by: Chris SchommerPries

DW.pdf (Fri May 29 14:22:40 2009) Linked to by: DijkgraafWitten theory

DamourSQC14.pdf (Tue May 27 12:18:23 2014) Linked to by: Uduality, quantum cosmology

DarkEnergyConcordance.gif (Wed Oct 26 03:51:28 2016)

DavidRoberts2014.jpg (Wed May 20 03:17:02 2015)

Davidovich.ps (Thu May 21 04:37:51 2009) Linked to by: Northwestern TFT Conference 2009

DayMonoidalLocaization73.pdf (Wed Jun 22 12:26:39 2016) Linked to by: monoidal localization

DessaiWittenGenus.pdf (Tue Mar 11 09:43:47 2014) Linked to by: Stolz conjecture

Directed_Graph_PQ_Difference_Conj.jpg (Sat Sep 19 15:20:22 2009)

Directed_Graph_PQ_Enlargement_Conj.jpg (Sat Sep 19 15:56:40 2009)

DuffBraneScan.jpg (Mon Jul 25 15:58:14 2016)

DuggerUniv.pdf (Mon Nov 9 23:51:55 2009) Linked to by: model structure on simplicial presheaves, geometric homotopy groups in an (infinity,1)topos, Universal Homotopy Theories, Čech model structure on simplicial presheaves

DylanWilsonOnANSS.pdf (Tue Feb 2 09:24:09 2016) Linked to by: Adams spectral sequence, Introduction to Stable Homotopy Theory

DylanWilsonProofOfLazard.pdf (Wed Feb 3 08:47:12 2016) Linked to by: Lazard's theorem

EDSnotes.pdf (Wed Sep 30 12:01:14 2009) Linked to by: exterior differential system

EhlersMScthesis.pdf (Thu Mar 10 15:06:14 2011) Linked to by: Phil Ehlers

Ehlersthesis (Fri Mar 19 09:36:32 2010)

Ehlersthesis.pdf (Fri Mar 19 11:07:06 2010) Linked to by: decalage, Phil Ehlers, join of simplicial sets

EpsilonDeltaBalls.png (Tue Jan 24 15:31:45 2017)

EsnaultAnalogy.pdf (Sun Aug 10 01:22:41 2014) Linked to by: function field analogy

EulerCharacteristicOfSpaceOfCurves.pdf (Tue Apr 1 01:58:34 2014) Linked to by: moduli space of curves, moduli stack of elliptic curves

FFRSStbl.gif (Sat Jun 13 16:12:54 2009) Linked to by: FRStheorem on rational 2d CFT

FFRSStbl.gif (Sat Jun 13 16:12:53 2009) Linked to by: FRStheorem on rational 2d CFT

FalkowskiLecture.pdf (Tue Sep 27 04:47:30 2011) Linked to by: HořavaWitten theory

FaulknerFerrar.pdf (Wed Feb 1 22:07:46 2012) Linked to by: exceptional Lie group

Field_Picture_PQ_Conjunction.jpg (Mon Sep 28 02:39:06 2009)

Field_Picture_PQ_Difference_Conjunction.jpg (Mon Sep 28 02:48:38 2009)

Field_Picture_PQ_Differential_Conjunction.jpg (Mon Sep 28 02:58:42 2009)

Field_Picture_PQ_Enlargement_Conjunction.jpg (Mon Sep 28 02:44:42 2009)

Field_Picture_PQ_Remainder_Conjunction.jpg (Mon Sep 28 03:02:23 2009)

Field_Picture_PQ_Tacit_Extension_Conjunction.jpg (Mon Sep 28 02:54:39 2009)

FigueroaElectromagneticDuality.pdf (Thu Jan 5 15:04:17 2017) Linked to by: electricmagnetic duality

Figure8Immersion.png (Sat May 6 11:35:44 2017)

Francis.ps (Fri May 22 06:01:08 2009) Linked to by: Northwestern TFT Conference 2009

FreedESI2012.pdf (Tue Apr 1 05:12:10 2014) Linked to by: type I string theory, super line 2bundle, orientifold, KR cohomology theory, type II string theory

Frobeniusreciprocity.pdf (Thu Aug 11 18:10:45 2011) Linked to by: Frobenius reciprocity

FundamentalGroupOfGenus2Surface.png (Tue Jan 24 13:00:17 2017)

Gadde2dTQFT.pdf (Wed May 14 07:41:44 2014) Linked to by: AGT correspondence

GalloziCSTTarski.pdf (Fri Oct 17 15:48:52 2014) Linked to by: relation between type theory and category theory

GathmannLocalization.pdf (Thu Jul 24 09:34:26 2014) Linked to by: localization of a ring, localization of a commutative ring, localization of a module

GeneralizedCohomology.pdf (Thu Nov 8 02:35:45 2012) Linked to by: multiplicative cohomology theory, ring spectrum, Brown representability theorem, suspension isomorphism, generalized (EilenbergSteenrod) cohomology

GeometricSupergravity.pdf (Wed Sep 30 12:20:40 2009) Linked to by: higher Cartan geometry, super Poincare Lie algebra, 11dimensional supergravity, Cartan geometry, Supergravity and Branes, D'AuriaFre formulation of supergravity, Linfinityalgebra, super Linfinity algebra, supergravity, Mtheory supersymmetry algebra, Fierz identity, GreenSchwarz action functional, Supergravity and Superstrings  A Geometric Perspective, 11d supergravity Lie 3algebra, geometry of physics  fundamental super pbranes, geometry of physics  superalgebra, Linfinity algebras in physics, supergravity Lie 6algebra, superCartan geometry

GeometricSupergravityErrata.pdf (Tue Jan 10 13:12:17 2017) Linked to by: D'AuriaFre formulation of supergravity, super Linfinity algebra, Fierz identity, geometry of physics  fundamental super pbranes, geometry of physics  superalgebra

GetzlerGoerss99.pdf (Sat Jan 16 02:39:14 2016) Linked to by: model structure on dgcoalgebras, differential graded coalgebra

GluingHemispheres.jpg (Tue Apr 5 11:54:53 2016)

GoerssOnBrownGitler.pdf (Wed Feb 3 12:51:44 2016) Linked to by: BrownGitler spectrum

GorbunovRaySpinBundles.pdf (Tue Sep 9 18:57:04 2014) Linked to by: spin group

GounelasBSD.pdf (Tue Aug 26 21:05:22 2014) Linked to by: Birch and SwinnertonDyer conjecture

GreenFunctionsAndPropagators.pdf (Wed Aug 27 07:49:51 2014) Linked to by: Feynman propagator

GriffithsPeriodsSummary.pdf (Tue Jun 17 01:00:47 2014) Linked to by: pconvex polarization, intermediate Jacobian

GrotendikTohoku.djvu (Tue Nov 24 12:32:38 2009)

GwilliamThesis.pdf (Wed Dec 21 05:10:01 2016) Linked to by: Owen Gwilliam, BVBRST formalism, Feynman diagram, free field theory, BeilinsonDrinfeld algebra, factorization algebra, factorization algebra of observables

HHRKervaire.pdf (Tue Apr 15 08:07:50 2014) Linked to by: equivariant cohomology, equivariant homotopy theory, Kervaire invariant, Mackey functor, ArfKervaire invariant problem, homotopy fixed point, KR cohomology theory

HQFTXMenagerie.pdf (Sat Feb 19 12:57:31 2011) Linked to by: Tim Porter, HQFT

HarpazStableInfinityCategory2013.pdf (Mon Oct 14 02:15:18 2013) Linked to by: stable (infinity,1)category, excisive (∞,1)functor

HatcherDiffeomorphismReview.pdf (Sun Nov 2 10:30:40 2014) Linked to by: diffeomorphism group

HausdorffProperty.png (Wed Apr 5 15:09:24 2017)

HeavisideFunction.png (Wed Apr 5 15:23:01 2017)

Hegel_taco.png (Thu Aug 27 21:12:41 2015) Linked to by: Hegelian taco

HermidaMakkaiPower01.pdf (Sat Nov 15 11:11:34 2014) Linked to by: opetopic omegacategory

HessLackBundCat.pdf (Wed Jan 14 21:26:10 2009) Linked to by: pointed set, generalized universal bundle

Higher_Order_Venn_Diagram.gif (Fri Oct 23 22:09:39 2009)

Higher_Order_Venn_Diagram.jpg (Sat Oct 24 00:05:56 2009)

Higher_Order_Venn_Diagram.png (Sat Oct 24 00:10:10 2009)

Higher_Order_Venn_Diagram.svg (Fri Oct 23 23:46:22 2009)

HoTTCoqcode.pdf (Tue Nov 8 21:50:43 2011) Linked to by: homotopy type theory

HoltenSpinningParticle.pdf (Wed Jul 27 00:07:17 2011)

Homeomorphism.png (Tue Jan 24 15:59:12 2017)

HomotopyEquivalentsToBiAnnulus.png (Mon Jan 23 12:28:24 2017)

HopfGaloisextensions.pdf (Wed Dec 17 01:55:01 2014)

HopfGaloisextensions.pdf (Tue Dec 16 22:28:26 2014)

HopfFibration.jpg (Fri Feb 5 05:58:37 2016)

HopkinsHoveyCobordismK.pdf (Wed Apr 23 22:18:26 2014) Linked to by: cobordism theory determining homology theory, Korientation

HopkinsLecture.pdf (Wed Jul 6 10:37:11 2016) Linked to by: Lazard's theorem

HuybrechtsLehn.pdf (Tue May 19 07:25:36 2015) Linked to by: Daniel Huybrechts, degree of a coherent sheaf, stable vector bundle, rank of a coherent sheaf, slope of a coherent sheaf, Narasimhan–Seshadri theorem

HuybrechtsLehn.pdf (Tue May 20 09:24:54 2014) Linked to by: Daniel Huybrechts, degree of a coherent sheaf, stable vector bundle, rank of a coherent sheaf, slope of a coherent sheaf, Narasimhan–Seshadri theorem

Hypostatic_Abstraction_Figure_1.jpg (Mon Sep 28 16:36:20 2009)

Hypostatic_Abstraction_Figure_2.jpg (Mon Sep 28 16:37:07 2009)

Hypostatic_Abstraction_Figure_3.jpg (Mon Sep 28 16:38:11 2009)

Hypostatic_Abstraction_Figure_4.jpg (Mon Sep 28 16:38:52 2009)

IbortMultisymplectic.pdf (Fri Dec 14 18:44:54 2012) Linked to by: G2, G2 manifold

Immersion.jpg (Sat May 6 11:07:19 2017)

Immersion.png (Sat May 6 11:10:30 2017)

InassaridzeOnKK.pdf (Wed Apr 3 01:17:27 2013) Linked to by: KKtheory

InflationPlanck2015.jpg (Fri May 12 15:26:21 2017)

IntersTh.pdf (Sat May 31 04:52:22 2014) Linked to by: intersection theory

IntroductionToHomologicalAlgebra161227.pdf (Tue Dec 27 07:19:37 2016)

IntroductionToHomologicalAlgebra170509.pdf (Tue May 9 11:08:42 2017) Linked to by: An Introduction to Homological Algebra, Introduction to Stable Homotopy Theory

IntroductionToOrbifolds.pdf (Sat Apr 5 03:18:11 2014) Linked to by: moduli stack of elliptic curves

IntroductionToStableHomotopyTheory11161227.pdf (Tue Dec 27 07:08:47 2016)

IntroductionToStableHomotopyTheory11170509.pdf (Tue May 9 09:53:09 2017) Linked to by: Introduction to Stable Homotopy Theory

IntroductionToStableHomotopyTheory12161227.pdf (Tue Dec 27 07:10:12 2016)

IntroductionToStableHomotopyTheory12170509.pdf (Tue May 9 10:00:14 2017) Linked to by: Introduction to Stable Homotopy Theory

IntroductionToStableHomotopyTheory170509.pdf (Tue May 9 10:29:56 2017) Linked to by: Introduction to Stable Homotopy Theory

IntroductionToStableHomotopyTheory2161227.pdf (Tue Dec 27 07:11:55 2016)

IntroductionToStableHomotopyTheory2170509.pdf (Tue May 9 10:10:13 2017) Linked to by: Introduction to Stable Homotopy Theory

IntroductionToStableHomotopyTheoryI161227.pdf (Tue Dec 27 07:10:38 2016)

IntroductionToStableHomotopyTheoryI170509.pdf (Tue May 9 10:05:32 2017) Linked to by: Introduction to Stable Homotopy Theory

IntroductionToStableHomotopyTheoryP161227.pdf (Tue Dec 27 07:03:15 2016) Linked to by: geometry of physics  homotopy types

IntroductionToStableHomotopyTheoryP170509.pdf (Tue May 9 09:47:44 2017) Linked to by: Introduction to Stable Homotopy Theory

IntroductionToStableHomotopyTheoryS161227.pdf (Tue Dec 27 07:16:34 2016) Linked to by: Introduction to Stable Homotopy Theory

IntroductionToStableHomotopyTheoryP161227.pdf (Tue Dec 27 06:47:23 2016)

IntroductionToTopologyI170417.pdf (Mon Apr 17 18:01:32 2017)

IntroductionToTopologyI170418.pdf (Tue Apr 18 04:57:18 2017)

IntroductionToTopologyI170418b.pdf (Tue Apr 18 08:41:37 2017)

IntroductionToTopologyI170418c.pdf (Tue Apr 18 08:55:39 2017)

IntroductionToTopologyI170419.pdf (Wed Apr 19 17:47:48 2017)

IntroductionToTopologyI170420.pdf (Thu Apr 20 03:41:49 2017)

IntroductionToTopologyI170420b.pdf (Thu Apr 20 06:39:51 2017)

IntroductionToTopologyI170420pdf (Thu Apr 20 03:40:32 2017)

IntroductionToTopologyI170424.pdf (Mon Apr 24 18:08:52 2017)

IntroductionToTopologyI170425.pdf (Tue Apr 25 10:45:32 2017)

IntroductionToTopologyI170427.pdf (Thu Apr 27 03:44:48 2017)

IntroductionToTopologyI170429.pdf (Sat Apr 29 04:55:50 2017)

IntroductionToTopologyI170429b.pdf (Sat Apr 29 16:28:34 2017)

IntroductionToTopologyI170501.pdf (Mon May 1 15:35:30 2017)

IntroductionToTopologyI170502.pdf (Tue May 2 05:57:33 2017)

IntroductionToTopologyI170502b.pdf (Tue May 2 13:51:39 2017)

IntroductionToTopologyI170503.pdf (Wed May 3 17:24:14 2017)

IntroductionToTopologyI170508.pdf (Mon May 8 04:36:01 2017)

IntroductionToTopologyI170509.pdf (Tue May 9 05:59:17 2017)

IntroductionToTopologyI170510.pdf (Wed May 10 09:28:07 2017)

IntroductionToTopologyI170511.pdf (Thu May 11 02:53:49 2017)

IntroductionToTopologyI170511b.pdf (Thu May 11 14:20:29 2017)

IntroductionToTopologyI170515.pdf (Mon May 15 15:31:00 2017)

IntroductionToTopologyI170516.pdf (Tue May 16 06:03:37 2017)

IntroductionToTopologyI170516b.pdf (Tue May 16 14:23:55 2017)

IntroductionToTopologyI170518.pdf (Thu May 18 04:12:04 2017)

IntroductionToTopologyI170522.pdf (Mon May 22 10:42:19 2017)

IntroductionToTopologyI170526.pdf (Wed Apr 26 06:33:39 2017)

IntroductionToTopologyI170529.pdf (Mon May 29 16:21:57 2017)

IntroductionToTopologyI170530.pdf (Tue May 30 06:04:29 2017)

IntroductionToTopologyI170530b.pdf (Tue May 30 09:21:01 2017)

IntroductionToTopologyI170601.pdf (Thu Jun 1 04:16:50 2017)

IntroductionToTopologyI170614.pdf (Wed Jun 14 11:35:17 2017)

IntroductionToTopologyI170620.pdf (Tue Jun 20 08:43:03 2017)

IntroductionToTopologyI170621.pdf (Wed Jun 21 16:33:01 2017)

IntroductionToTopologyI170629.pdf (Thu Jun 29 06:30:01 2017)

IntroductionToTopologyI170704.pdf (Tue Jul 4 05:58:01 2017) Linked to by: Introduction to Topology

IntroductionToTopologyI180417.pdf (Tue Apr 18 04:53:47 2017)

IntroductionToTopologyII170711.pdf (Tue Jul 11 10:45:24 2017)

IntroductionToTopologyII170718.pdf (Mon Jul 17 18:30:52 2017)

IntroductionToTopologyII170718b.pdf (Tue Jul 18 05:41:51 2017)

IntroductionToTopologyII170719.pdf (Wed Jul 19 16:35:56 2017)

IntroductionToTopologyII170720.pdf (Thu Jul 20 08:30:05 2017) Linked to by: Introduction to Topology

IntroductionToTopologyII171007.pdf (Mon Jul 10 05:51:02 2017)

IsaksenANSSE2p.jpg (Thu Feb 4 12:54:35 2016)

IsaksenANSSEinfinityp.jpg (Thu Feb 4 12:55:00 2016)

IselyKTheory.pdf (Wed Sep 3 18:10:46 2014) Linked to by: algebraic Ktheory

IsonoSlides.pdf (Sun May 11 03:05:04 2014) Linked to by: Mwave

JLTBaumConnesForGroupoids.pdf (Tue Jul 9 22:04:26 2013) Linked to by: BaumConnes conjecture

JacobiatorIdentity.jpg (Tue Nov 8 05:57:24 2016)

JacobsCategoricalTypeTheory.pdf (Thu May 10 15:18:19 2012) Linked to by: type theory

JardenNormedRings.pdf (Sun Jul 13 23:25:05 2014) Linked to by: normed ring

JardineBrownrep.pdf (Tue Sep 22 13:13:18 2009)

JardineModelDG.pdf (Thu Oct 29 01:06:34 2009) Linked to by: model structure on dgalgebras, model structure on chain complexes

JoshuaDuality.pdf (Wed Dec 4 13:57:14 2013) Linked to by: Grothendieck duality, six operations, VerdierGrothendieck context, Verdier duality

JoyalThetaCategories.pdf (Tue Nov 13 19:52:55 2012) Linked to by: ball, Theta category

KtheoryandMoritaTheoryrevised.pdf (Wed Dec 17 15:49:21 2014)

KtheoryandMoritaTheory.pdf (Tue Dec 16 22:28:16 2014)

KtheoryandMoritaTheory.pdf (Wed Dec 17 01:54:24 2014)

K6associativity.pdf (Thu Jun 11 21:42:27 2009) Linked to by: tetracategory

Kanpull.pdf (Wed May 27 12:07:34 2009)

Kantization09May27.pdf (Wed May 27 18:30:19 2009) Linked to by: 2009 June changes

KeplerPlatonic.jpg (Fri Feb 5 06:10:33 2016)

KhesinWendt08.pdf (Thu May 15 02:06:14 2014) Linked to by: holomorphic ChernSimons theory

KillingSpinors.pdf (Fri Sep 12 11:56:07 2014) Linked to by: Killing spinor

KirbyMelvon3Framings.pdf (Tue Sep 9 06:51:43 2014) Linked to by: framed manifold

Kitada75.pdf (Fri Mar 21 08:31:46 2014) Linked to by: Spin^c Dirac operator

KleinRetyped.pdf (Wed Dec 17 20:56:47 2014) Linked to by: symmetry, Klein geometry, stabilizer group, Erlangen program

Kleinschmidt12.pdf (Fri May 16 09:42:45 2014) Linked to by: Uduality

KockMonoidalMonads.pdf (Wed Feb 12 08:55:52 2014) Linked to by: commutative algebraic theory

KontsevichRosenbergNCSpaces.pdf (Tue Apr 12 18:47:21 2011) Linked to by: infinitesimal extension, Qcategory, formally étale morphism of schemes, formally etale morphism

KoppEntropy.pdf (Sat Feb 1 12:45:12 2014)

KreckStolzElliptic.pdf (Wed Apr 23 13:20:23 2014) Linked to by: spin orientation of elliptic cohomology, elliptic genus, cobordism theory determining homology theory

KuismanenBaryogenesis.pdf (Tue Sep 16 10:31:12 2014) Linked to by: baryogenesis

LawvereCohesiveToposes.pdf (Sat Oct 8 02:23:50 2011) Linked to by: cohesive topos, Cohesive Toposes and Cantor's "lauter Einsen", William Lawvere, adjoint modality, Higher toposes of laws of motion, ETCS

LawvereComprehension.pdf (Mon Jan 20 13:04:56 2014) Linked to by: logic, axiom of separation, William Lawvere

LawvereSDGOutline.pdf (Wed Jun 5 22:57:14 2013) Linked to by: synthetic differential geometry

LawvereToposesOfLawsOfMotions.pdf (Wed Jun 5 22:51:57 2013) Linked to by: synthetic differential geometry

LeinsterYoneda.ps (Sun Jan 11 18:11:21 2009) Linked to by: Yoneda lemma

LevineMotiveLecture.pdf (Sat Feb 8 11:51:33 2014) Linked to by: motive

LineWithTwoOrigins.png (Thu Apr 13 04:17:44 2017)

LipshitzRobinson.pdf (Fri Mar 30 07:37:39 2012) Linked to by: polydisc

LipskiThesis.pdf (Wed Jun 13 19:52:19 2012)

LipskyThesis.pdf (Wed Jun 13 19:53:38 2012) Linked to by: higher parallel transport, fiber integration in ordinary differential cohomology

LocalizationOfModelCategories.pdf (Tue Oct 30 14:16:54 2012) Linked to by: localization of model categories

LoefflerAutomorphic.pdf (Tue Sep 9 06:12:08 2014) Linked to by: automorphic form

LoomisSternberg13s2.djvu (Fri Sep 2 20:09:59 2011) Linked to by: Lagrange multiplier

LumsdaineWarren2013.pdf (Wed May 7 20:38:14 2014) Linked to by: substitution, relation between type theory and category theory

LurieCrystals.pdf (Wed Jun 7 02:45:12 2017) Linked to by: crystalline cohomology

LurieLecture1.ps (Tue May 19 13:12:55 2009) Linked to by: Northwestern TFT Conference 2009

LurieLecture2.ps (Wed May 20 13:17:40 2009) Linked to by: Northwestern TFT Conference 2009

LurieLecture3.ps (Fri May 22 06:00:23 2009) Linked to by: Northwestern TFT Conference 2009

LurieLecture4.ps (Fri May 22 15:34:31 2009) Linked to by: Northwestern TFT Conference 2009

MAXIMISED.vanilla.print.css (Fri Apr 6 04:52:16 2012)

MacLaneBowdoinLectures69.pdf (Mon Apr 17 16:50:53 2017) Linked to by: Lectures on category theory

MagicPyramid.jpg (Sat Sep 17 17:39:55 2016)

MandelbrotSet.png (Mon May 15 06:28:31 2017)

MapOfE6.png (Wed Feb 1 03:33:18 2017)

MartinecD1D5.pdf (Thu May 7 09:03:45 2015) Linked to by: D1D5 brane bound state

MarvanJetComonad.pdf (Wed May 13 11:24:09 2015) Linked to by: differential operator, differential equation, jet bundle

MarvanJetComonadPDE.pdf (Thu Oct 6 03:15:16 2016) Linked to by: jet comonad

MarvanThesis.pdf (Thu Oct 6 03:09:26 2016) Linked to by: jet comonad

McMillanNNTheorem.pdf (Wed May 21 04:36:25 2014) Linked to by: NewlanderNirenberg theorem

MelliesContinuation.pdf (Wed Feb 12 01:40:29 2014) Linked to by: continuation monad

MendlerComputationalTypeTheory.pdf (Sun Jan 12 10:43:01 2014) Linked to by: computational type theory

Meng.djvu (Thu Nov 6 17:18:30 2014) Linked to by: convex space, metric space

MeyerMoritaEquivalence.pdf (Wed Apr 3 17:47:21 2013) Linked to by: Morita equivalence

Minimal_Negation_Operator_lPcQcRr.jpg (Mon Sep 28 03:08:20 2009)

ModelCatPrimer.pdf (Wed Feb 11 10:21:13 2009) Linked to by: model category

MoebiusStripAsQuotientOfSquare.png (Tue Jan 24 12:37:56 2017)

MoerdijkCyclic.pdf (Sun Mar 30 23:57:18 2014) Linked to by: classifying topos, abstract circle, cyclic set

MolotkovSupermanifolds.pdf (Sat Apr 2 08:38:38 2011)

MonodromyOfEllipticSurfaces.pdf (Fri Apr 11 02:43:10 2014) Linked to by: elliptic fibration

MooijGUT.pdf (Tue Sep 2 17:07:07 2014) Linked to by: gauge coupling unification

Morrow17.pdf (Thu Feb 23 04:35:51 2017)

NeighbourhoodsAndOpenBalls.png (Tue Jan 24 14:34:59 2017)

NicolaiTalk14.pdf (Tue May 27 12:24:08 2014) Linked to by: Uduality

NielsenChuangQuantumComputation.pdf (Sat Jan 18 07:36:18 2014) Linked to by: quantum operation, quantum computation

NikolausHigherCatStructuresInGeometry.pdf (Fri Jul 1 16:22:59 2011) Linked to by: Thomas Nikolaus

NikolausHigherCatStructuresInGeometrySlides.pdf (Fri Jul 1 16:38:19 2011) Linked to by: Thomas Nikolaus

Notes_on_Set_Theory.pdf (Sun Dec 14 23:22:49 2014)

Notes_on_Set_Theory1.pdf (Sun Dec 14 23:25:57 2014)

Novikov67.pdf (Fri Apr 8 05:35:33 2016) Linked to by: Adams spectral sequence, Adams–Novikov spectral sequence

OctahedralProofFromPastingPushouts.jpg (Mon Jun 13 10:47:24 2016)

OctonionMultiplicationTable.jpg (Wed Dec 14 13:41:11 2016)

OldBraneScan.jpg (Tue Jan 10 17:49:52 2017)

OpenSubsetsOfSquareInsidePlane.png (Tue Jan 24 15:45:50 2017)

PedrotticECohomology2016.pdf (Fri Jun 17 12:07:22 2016) Linked to by: complex oriented cohomology theory, ConnerFloyd Chern class, Riccardo Pedrotti, Introduction to Cobordism and Complex Oriented Cohomology, Thom isomorphism, complex projective space

Piazenza91.pdf (Wed Apr 13 13:58:15 2016) Linked to by: model structure on functors, Model categories of diagram spectra, Robert Piacenza, Elmendorf's theorem, classical model structure on topological spaces

PlanckData.jpg (Fri May 12 15:22:44 2017)

PorterDipath.pdf (Thu Jan 15 20:03:39 2009) Linked to by: causet

ProductTopology.png (Tue Jan 24 15:27:27 2017)

PuppeStableHomotopyCategory.pdf (Wed Jun 19 00:18:01 2013) Linked to by: stable homotopy theory, smash product of spectra, stable homotopy category

PursuingStacks.tar.gz (Fri Jul 31 16:35:42 2015) Linked to by: Pursuing Stacks

QuaternionMultiplicationTable.jpg (Wed Dec 14 13:40:30 2016)

QuillenModulesOverRngs.pdf (Wed Aug 20 00:47:10 2014) Linked to by: nonunital ring, torsion module

QuineZetaRegularization.pdf (Mon Aug 25 05:06:29 2014) Linked to by: zeta function of an elliptic differential operator

QuotientOfSquareIsCylinderAndTorus.png (Tue Jan 24 15:37:06 2017)

Rewritingandhomotopy.pdf (Mon Feb 27 21:16:20 2012) Linked to by: Tim Porter

RingsOfSmoothFunctionsI.pdf (Wed Feb 3 15:22:29 2010) Linked to by: smooth algebra

RobbinSalamonMetaplectic.pdf (Thu Jan 1 18:34:56 2015) Linked to by: path integral, quantomorphism group, quadratic Hamiltonian, metaplectic group, metaplectic representation, HamiltonJacobi equation, extended affine symplectic group

RobbinSalamonPhaseFunctionsPathIntegrals.djvu (Thu Nov 25 17:43:45 2010) Linked to by: Joel Robbin, Dietmar Salamon

RobbinSalamonPhaseFunctionsPathIntegrals.djvu (Thu Nov 25 17:41:06 2010) Linked to by: Joel Robbin, Dietmar Salamon

RobertsStringS5.pdf (Wed Jul 2 00:24:31 2014) Linked to by: string structure

RoblesZetaRegularization.pdf (Wed Aug 27 12:25:45 2014) Linked to by: zeta function regularization

RogersGottingen11.pdf (Tue Mar 28 13:33:13 2017) Linked to by: higher geometric quantization

RognesSphereSpectrum.pdf (Mon Jun 24 15:49:11 2013) Linked to by: sphere spectrum

Rooted_Edge.jpg (Wed Sep 16 19:12:33 2009)

Rooted_Node.jpg (Wed Sep 16 19:10:45 2009)

Scatnotes.pdf (Fri Feb 12 22:06:41 2010)

SaemannCQSYMP16.pdf (Wed Jul 27 04:37:47 2016) Linked to by: string theory FAQ

SaizStableBundles.pdf (Mon Jul 14 05:15:51 2014) Linked to by: stable vector bundle, GITstable point, geometric invariant theory

SchenkelTrento14.pdf (Mon Sep 15 08:43:28 2014)

SchenkelTrento2014.pdf (Mon Sep 15 10:56:42 2014) Linked to by: AQFT, quantum field theory, field bundle, homotopical algebraic quantum field theory, locally covariant perturbative quantum field theory

SchneiderBeilinsonConjectures.pdf (Mon Jul 14 23:45:56 2014) Linked to by: Beilinson conjecture

SchommerPriesDefects.pdf (Thu Jul 7 16:17:54 2011) Linked to by: holographic principle of higher category theory, holographic principle

Schreiber2States.pdf (Mon Nov 28 21:56:35 2011) Linked to by: twisted bundle

SchreiberOberwolfachJune2009Wall.pdf (Tue Jun 9 18:13:54 2009)

SchwarzhauptMasseyDeligne.pdf (Thu Dec 13 05:36:32 2012) Linked to by: Massey product

SeelyLinearLogic.pdf (Mon Dec 9 06:23:14 2013) Linked to by: starautonomous category, linear logic, relation between type theory and category theory, linear type theory

Segal72.pdf (Tue May 30 11:27:10 2017) Linked to by: Snaith theorem, KahnPriddy theorem, complex projective space

SegalCategoriesAndCohomologyTheories.pdf (Fri Feb 18 19:35:39 2011) Linked to by: geometric realization of simplicial topological spaces

SelingerPositiveMaps.pdf (Sat Jan 18 06:58:18 2014) Linked to by: quantum operation, Geometry of Interaction

SelingerSelfDual.pdf (Sat Jan 25 14:07:53 2014) Linked to by: daggercompact category, selfdual object

SelingerThesis.pdf (Fri Jan 31 08:59:44 2014) Linked to by: bilimit

SeminarTopologie2017.png (Wed Feb 1 23:58:36 2017)

ShrinkingBalls.png (Tue Jan 24 16:40:03 2017)

SiuHigherTheta.pdf (Mon Sep 22 12:17:21 2014) Linked to by: theta function

SjamaarOrbitMethod.pdf (Mon Jul 2 19:31:23 2012) Linked to by: orbit method

SnakeLemma.png (Fri Aug 24 18:46:54 2012) Linked to by: snake lemma

SouriauPrequantumFlowChart.jpg (Sat Oct 3 03:57:00 2015)

StableChromaticGlossary.pdf (Fri May 2 05:07:22 2014) Linked to by: ring spectrum, stable homotopy theory, chromatic homotopy theory

StableComplexSpinC.pdf (Wed Nov 7 02:24:47 2012) Linked to by: spin^c structure, geometric quantization by pushforward, stable complex structure

StasheffCohomPhysicsSurvey.pdf (Sun May 24 13:53:01 2009) Linked to by: A Survey of Cohomological Physics

StasheffHomotopyStructuresReview.pdf (Wed Jan 20 04:11:21 2016) Linked to by: A Survey of Cohomological Physics, Linfinityalgebra, Linfinity algebras in physics

StasheffParallelTransportv01.pdf (Fri Jan 7 19:46:01 2011)

StasheffParallelTransportv02.pdf (Sun Jan 23 21:40:49 2011) Linked to by: higher parallel transport

StasheffSOn.pdf (Tue Aug 6 16:50:09 2013) Linked to by: special orthogonal group

SteenrodOnCohomologyOperations.pdf (Wed Nov 11 19:59:10 2009) Linked to by: cochain on a simplicial set

StereographicProjection.png (Sun May 7 08:40:00 2017)

StiXGaloisAndGT.pdf (Mon Jun 16 04:45:33 2014) Linked to by: GrothendieckTeichmüller tower, absolute Galois group

String.gif (Sun Mar 7 19:31:48 2010)

StringSMatrixFromPolchinski.jpg (Tue Sep 20 12:09:36 2016)

StringSMatrixSuperFromPolchinski.jpg (Tue Sep 20 12:30:16 2016)

Submersion.jpg (Sat May 6 11:07:37 2017)

Submersion.png (Sat May 6 11:11:04 2017)

SujahtaElliptic.pdf (Fri May 23 05:04:51 2014) Linked to by: elliptic curve

Surfaces.png (Sat Apr 29 04:16:26 2017)

SymmetricSpectra.pdf (Fri Dec 4 16:05:22 2009) Linked to by: symmetric smash product of spectra

Szabo09.pdf (Fri Jul 24 09:40:09 2009) Linked to by: brane, Dbrane

TammeRegulator.pdf (Tue Apr 29 04:08:04 2014) Linked to by: higher regulator

TangentSpaceToSphere.png (Tue Feb 7 10:53:03 2017)

TaubNUT.png (Sat Jul 15 17:22:30 2017)

TetracategoricalData.pdf (Thu Jun 11 21:41:46 2009) Linked to by: tetracategory

The3SheetedCoveringsOfTheCircle.png (Tue Jan 24 06:11:52 2017)

TheMTheoryAmoeba.jpg (Tue Jan 10 18:20:20 2017)

ThorpeParallelizable.pdf (Thu Sep 11 15:26:43 2014) Linked to by: teleparallel gravity, framed manifold

ThreeNonHomeoButHomotopyEquivGraphs.png (Mon Jan 23 13:57:26 2017)

ToenLecture1.ps (Wed May 20 13:20:04 2009) Linked to by: Northwestern TFT Conference 2009

ToenLecture2.ps (Wed May 20 13:22:02 2009) Linked to by: Northwestern TFT Conference 2009

ToenLecture3.ps (Fri May 22 06:00:45 2009) Linked to by: Northwestern TFT Conference 2009

ToenLecture4.ps (Fri May 22 17:07:58 2009) Linked to by: Northwestern TFT Conference 2009

ToenStacksNAC.pdf (Thu Jan 8 21:09:06 2009) Linked to by: infinitystack homotopically

TopologiesOn3ElementSet.png (Tue Jan 24 15:18:26 2017)

ToppanClassicalAnomaly.pdf (Fri Sep 13 01:06:03 2013) Linked to by: classical anomaly

TorusAsQuotientOfSquare.png (Tue Jan 24 12:34:38 2017)

TwistorSpaceCorrespondence.jpg (Tue Oct 18 15:39:34 2016)

U52unitcondition.pdf (Thu Jun 11 21:43:09 2009) Linked to by: tetracategory

U53unitcondition.pdf (Thu Jun 11 21:43:40 2009)

U53unitconditionA.pdf (Thu Jun 11 21:46:23 2009) Linked to by: tetracategory

U54unitcondition.pdf (Thu Jun 11 21:44:19 2009) Linked to by: tetracategory

UniversalCoveringOfCircle.png (Tue Jan 24 12:23:35 2017)

UrysohnConstruction.png (Fri Apr 28 11:38:06 2017)

VanKoughnettLocalization.pdf (Fri Jul 25 09:57:56 2014) Linked to by: Moore spectrum, fracture theorem, Bousfield localization of spectra

VariationalBicomplex.jpg (Mon Dec 19 13:05:32 2016)

Venn_Diagram_4_Dimensions_Bare_Cacti_8_Inch.gif (Sat Oct 24 15:30:14 2009)

Venn_Diagram_4_Dimensions_Bare_Cacti_8_Inch.jpg (Sat Oct 24 15:33:48 2009)

Venn_Diagram_4_Dimensions_Bare_Cacti_8_Inch.png (Sat Oct 24 15:37:55 2009)

Venn_Diagram_4_Dimensions_UV_Cacti_8_Inch.gif (Sat Oct 24 19:50:14 2009)

Venn_Diagram_4_Dimensions_UV_Cacti_8_Inch.jpg (Sat Oct 24 19:56:40 2009)

Venn_Diagram_4_Dimensions_UV_Cacti_8_Inch.png (Sat Oct 24 20:01:36 2009)

Venn_Diagram_4_Dimensions_Version_1.gif (Sat Oct 24 02:52:19 2009)

Venn_Diagram_4_Dimensions_Version_1.jpg (Sat Oct 24 02:55:49 2009)

Venn_Diagram_4_Dimensions_Version_1.png (Sat Oct 24 02:59:59 2009)

Venn_Diagram_4_Dimensions_Version_1.svg (Sat Oct 24 03:22:37 2009)

Venn_Diagram_F_Equals_P_And_Q.jpg (Sat Sep 19 04:10:57 2009)

Venn_Diagram_PQ_Difference_Conj.jpg (Sat Sep 19 15:17:07 2009)

Venn_Diagram_PQ_Difference_Conj_At_Conj.jpg (Sat Sep 19 13:04:57 2009)

Venn_Diagram_P_And_Q.jpg (Fri Sep 18 15:22:24 2009)

Venn_Diagram_P_Q_dP_dQ.jpg (Sat Sep 19 12:45:15 2009)

Venn_Diagram_lPcQcRr.jpg (Tue Oct 27 02:40:20 2009)

Venn_Diagram_llPrclQrclRrr.jpg (Tue Oct 27 02:42:30 2009)

VerityDescent.pdf (Thu Jul 23 14:19:09 2009) Linked to by: Verity on descent for strict omegagroupoid valued presheaves

VizmanQuantomorphism.pdf (Wed Jun 27 12:20:29 2012) Linked to by: quantomorphism group

WadlerMonads.pdf (Mon Jan 13 04:17:34 2014) Linked to by: monad (in computer science)

WaldorfTalbot2010.pdf (Tue Dec 20 01:50:40 2011) Linked to by: Topological Quantum Field Theories from Compact Lie Groups

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WeakGravityConjectureHetStates.jpg (Tue Jun 27 09:01:58 2017)

WijnholtCompactification14.pdf (Mon Jun 16 08:04:24 2014) Linked to by: supersymmetry and CalabiYau manifolds, Ftheory, string phenomenology, Martin Wijnholt

WilczekGaugeCouplingUnification.pdf (Tue Sep 2 16:47:28 2014) Linked to by: gauge coupling unification

Witten84.pdf (Tue Sep 30 15:09:47 2014) Linked to by: string theory

WittenCQFT.pdf (Fri May 2 01:41:40 2014) Linked to by: topological quantum field theory, topologically twisted D=4 super YangMills theory, FQFT, TCFT, topological twist, cohomological field theory, 2d TQFT

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WittenOnJonesPolynomial2013.pdf (Fri Oct 4 03:55:12 2013) Linked to by: Jones polynomial, Khovanov homology

WittenOnKhovanovHomology2013.pdf (Fri Oct 4 03:55:57 2013) Linked to by: Jones polynomial, Khovanov homology

Wockel.pdf (Mon May 25 03:48:34 2009) Linked to by: Northwestern TFT Conference 2009

WrightIwasawaTate.pdf (Sun Aug 24 23:20:14 2014) Linked to by: IwasawaTate theory

YanagidaBaryogenesis.pdf (Mon Sep 15 22:34:23 2014) Linked to by: baryogenesis

YonedaObituary.jpg (Mon Oct 19 04:28:05 2015)

ZuckermanVariation.pdf (Wed May 4 11:04:47 2011) Linked to by: Gregg Zuckerman, phase space, variational calculus, conserved current, variational bicomplex, ChernSimons theory, source form, EulerLagrange form, Lepage form

adamstypedifferentials.jpg (Fri Feb 12 11:19:11 2016)

adjunctionL.png (Sun Oct 4 19:27:26 2009) Linked to by: adjunction

adjunctionR.png (Sun Oct 4 19:27:55 2009) Linked to by: adjunction

adjunctioncounit.png (Sun Oct 4 19:29:00 2009) Linked to by: adjunction

adjunctiondownstringminimal.png (Sun Oct 4 19:31:09 2009) Linked to by: adjunction, triangle identities

adjunctiondownstring.png (Sun Oct 4 19:30:11 2009) Linked to by: adjunction, triangle identities

adjunctionunit.png (Sun Oct 4 19:28:34 2009) Linked to by: adjunction

adjunctionupstringminimal.png (Sun Oct 4 19:30:43 2009) Linked to by: adjunction, triangle identities

adjunctionupstring.png (Sun Oct 4 19:30:00 2009) Linked to by: adjunction, triangle identities

alt_functor.jpg (Sat Nov 7 23:33:56 2009)

altfunctor.jpg (Sat Mar 27 14:33:11 2010)

apstalk.pdf (Sun Mar 21 22:55:58 2010)

apstalk2.pdf (Fri Jul 2 17:24:03 2010)

arXiv_icon.gif (Wed Dec 3 19:04:24 2008)

arcdiagram.png (Tue Sep 1 01:28:04 2015)

bergner.pdf (Tue Jun 2 09:14:54 2009) Linked to by: Northwestern TFT Conference 2009

bimonoidcounitlhs.png (Tue Jun 16 09:36:28 2015)

bimonoidcounitrhs.png (Tue Jun 16 09:36:53 2015)

bimonoideq1.png (Tue Jun 16 09:55:11 2015)

bimonoideq1.svg (Tue Jun 16 10:03:42 2015)

bimonoideq2.png (Tue Jun 16 09:55:33 2015)

bimonoideq2.svg (Tue Jun 16 10:04:11 2015)

bimonoideq3.png (Tue Jun 16 09:55:50 2015)

bimonoideq3.svg (Tue Jun 16 10:04:30 2015)

bimonoideq4.png (Tue Jun 16 10:20:57 2015)

bimonoidlhs.pdf (Tue Jun 16 09:01:39 2015)

bimonoidlhs.png (Tue Jun 16 09:09:34 2015)

bimonoidrhs.pdf (Tue Jun 16 09:02:11 2015)

bimonoidrhs.png (Tue Jun 16 09:09:18 2015)

bimonoidunitlhs.png (Tue Jun 16 09:35:40 2015)

bimonoidunitrhs.png (Tue Jun 16 09:36:01 2015)

bondalKaprEnhTRiangCat.pdf (Wed Apr 29 15:45:54 2009) Linked to by: pretriangulated dgcategory, pretriangulated dgcategory, twisted complex, dgcategory

branescan.gif (Mon Oct 25 23:10:41 2010) Linked to by: double dimensional reduction, brane

bvaxes.svg (Sun Jun 12 11:53:44 2011)

bvdiag.svg (Sun Jun 12 11:44:40 2011)

cardy_condition.jpg (Thu Nov 20 16:50:30 2014) Linked to by: Cardy condition

cech.pdf (Sat Jul 18 15:25:24 2009)

chorddiagram.png (Tue Sep 1 01:28:40 2015)

chorddiagram.svg (Sat Sep 5 00:04:34 2015)

circle.pdf (Sun Feb 28 17:16:53 2010) Linked to by: Warsaw circle

commutative_law.jpg (Tue Jul 20 03:52:22 2010) Linked to by: Frobenius algebra

commuteloop.jpg (Sun Mar 28 15:51:42 2010)

comonoid_laws.jpg (Tue Jul 20 03:50:50 2010) Linked to by: Frobenius algebra

cosmiccube.jpg (Thu Jul 15 08:46:14 2010) Linked to by: cosmic cube

costello.pdf (Thu May 28 15:24:31 2009) Linked to by: Northwestern TFT Conference 2009, factorization algebra, factorization algebra of observables

cqarr.svg (Sun Jun 12 11:54:34 2011)

cylinder.jpg (Thu May 25 10:33:20 2017)

delooping1.jpg (Thu Jul 2 15:40:55 2009)

delooping2.jpg (Thu Jul 2 15:53:30 2009)

diagram1.jpg (Wed May 7 23:20:38 2014)

diagram2.jpg (Wed May 7 23:31:23 2014)

doublecategorypinwheel.png (Tue Apr 6 03:47:21 2010) Linked to by: double category

dumbbellFeynmanDiagramm.png (Tue Nov 17 04:11:49 2015)

dumbbellFeynmandiagram.png (Tue Nov 17 04:03:13 2015)

eric.jpg (Fri Oct 9 06:35:32 2009) Linked to by: Eric Forgy

explode.jpg (Thu May 28 17:18:51 2009)

faceanddegeneracymaps.jpg (Thu Feb 18 07:17:26 2016)

faceanddegeneracymaps.jpg (Thu Feb 18 07:17:23 2016)

fig1.gif (Sat Aug 27 13:58:33 2011)

fig6_10c2.jpg (Mon Feb 16 18:10:35 2009)

frobenius_algebra.jpg (Tue Jul 20 03:37:59 2010) Linked to by: FQFT, Frobenius algebra

frobenius_laws.jpg (Tue Jul 20 03:51:37 2010) Linked to by: Frobenius algebra

functor.jpg (Sun Mar 28 01:38:52 2010)

general.css (Tue Dec 2 23:09:28 2008) Linked to by: General Discussion

if.pdf (Sun Jan 4 18:58:51 2009) Linked to by: 2009 January changes

implode.jpg (Fri May 29 17:40:19 2009)

jibladzeCoeffLargeCats.djvu (Mon Aug 3 14:39:49 2009) Linked to by: crossed profunctor, 2009 August changes

jpg (Mon Oct 19 04:25:08 2015)

kan0.png (Sun Mar 29 19:10:35 2009) Linked to by: Kan extension

kan1.png (Sun Mar 29 19:10:59 2009) Linked to by: Kan extension

kan2.png (Sun Mar 29 19:11:16 2009) Linked to by: Kan extension

kong.pdf (Fri May 29 20:43:51 2009) Linked to by: Northwestern TFT Conference 2009

krasauskas.pdf (Thu Mar 19 23:02:22 2009) Linked to by: cycle category, skewsimplicial set, 2009 March changes

lawvereprobability1962.pdf (Mon Oct 13 08:08:42 2014) Linked to by: Giry monad

laxadjmdfs.png (Fri May 1 19:18:23 2009) Linked to by: lax 2adjunction

laxadjswlwtleps.png (Fri May 1 19:19:14 2009) Linked to by: lax 2adjunction

laxadjswlwtleta.png (Fri May 1 19:18:52 2009) Linked to by: lax 2adjunction

lctvs.dot (Tue May 11 14:19:47 2010)

lettrejoyal.pdf (Fri Dec 19 15:11:01 2014) Linked to by: Andre Joyal

lnarr.svg (Sun Jun 12 11:54:17 2011)

lurie.pdf (Thu May 28 15:25:12 2009) Linked to by: Northwestern TFT Conference 2009, geometric Satake equivalence

mappingcone.jpg (Thu Feb 18 06:27:19 2016)

mathphysphil.pdf (Thu Jan 29 11:17:16 2009)

matrixcalculus.pdf (Mon Mar 30 16:31:50 2009) Linked to by: matrix calculus

menagerie10.pdf (Fri Mar 5 19:58:16 2010)

menagerie10a.pdf (Sat Mar 27 16:43:16 2010) Linked to by: Crossed Menagerie

moebiusstrip.jpg (Thu May 25 10:35:11 2017)

monadaxiomsunlabeled.png (Fri Oct 9 01:05:59 2009) Linked to by: monad

monaddatalabeled.png (Fri Oct 9 01:03:04 2009) Linked to by: monad

monaddataunlabeled.png (Fri Oct 9 01:05:33 2009) Linked to by: monad

monoidaxiomsunlabeled.png (Fri Oct 16 20:17:36 2009) Linked to by: monoid

monoiddatalabeled.png (Fri Oct 16 20:16:52 2009) Linked to by: monoid

monoiddataunlabeled.png (Fri Oct 16 20:17:19 2009) Linked to by: monoid

monoid_laws.jpg (Tue Jul 20 03:49:54 2010) Linked to by: FQFT, Frobenius algebra

multispansJan24.pdf (Sat Jan 24 12:36:36 2009)

multispansJan24b.pdf (Sat Jan 24 19:04:48 2009)

ncafe_5.gif (Wed Dec 3 18:52:04 2008)

ncafe_small.gif (Wed Dec 3 18:11:48 2008)

ncafeicon_small.gif (Wed Dec 3 18:45:24 2008)

n.png (Sat Nov 29 19:24:26 2008)

naturalitysquare000.pdf (Mon Jun 5 13:17:04 2017)

naturalitysquare001.pdf (Mon Jun 5 13:42:15 2017)

nforumcommentsearch.xml (Wed Oct 14 19:42:11 2009) Linked to by: How To

nforumtopicsearch.xml (Wed Oct 14 19:40:57 2009) Linked to by: How To

nlabedit.xml (Sat Aug 29 01:36:58 2009) Linked to by: How To

nlabedit.xml (Mon Oct 19 14:00:06 2009) Linked to by: How To

nlabgoto.xml (Wed Apr 29 21:15:37 2009) Linked to by: How To

nlabsearch.xml (Wed Apr 29 21:14:34 2009) Linked to by: How To

notWISC.pdf (Thu Nov 8 05:05:06 2012)

notWISC2.pdf (Thu Nov 8 08:09:44 2012)

oberwolfach_bunke.pdf (Thu Jun 11 16:52:22 2009)

oberwolfach_costello1.pdf (Wed Jun 10 22:43:40 2009)

oberwolfach_costello2.pdf (Wed Jun 10 22:44:33 2009)

oberwolfach_costello3.pdf (Wed Jun 10 22:45:04 2009)

oberwolfach_freed.pdf (Wed Jun 10 22:42:02 2009)

oberwolfach_june2009_bunke.pdf (Sat Jun 13 10:14:30 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_costello1.pdf (Sat Jun 13 10:15:59 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_costello2.pdf (Sat Jun 13 10:16:18 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_costello3.pdf (Sat Jun 13 10:17:04 2009)

oberwolfach_june2009_freed.pdf (Sat Jun 13 10:17:45 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_freed_extra.pdf (Mon Jun 15 09:27:36 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_henriques_extra.pdf (Mon Jun 15 09:29:01 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_henriques_pavlov.pdf (Sat Jun 13 10:56:16 2009)

oberwolfach_june2009_hopkins.pdf (Sat Jun 13 10:18:12 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_hopkins.pdf (Sat Jun 13 10:18:44 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_kahle.pdf (Sat Jun 13 10:17:42 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_pavlov_costello.pdf (Mon Jun 15 13:14:50 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_pavlov_freed.pdf (Mon Jun 15 13:15:18 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_pavlov_kahle.pdf (Mon Jun 15 13:14:24 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_pavlov_schick.pdf (Mon Jun 15 13:13:08 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_pavlov_schweigert_runkel.pdf (Mon Jun 15 13:13:36 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_pavlov_wilson.pdf (Mon Jun 15 13:12:44 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_redden.pdf (Sat Jun 13 10:17:49 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_runkel.pdf (Sat Jun 13 10:13:02 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_schick.pdf (Sat Jun 13 10:15:41 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_schreiber.pdf (Mon Jun 15 09:23:36 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_schweigert.pdf (Sat Jun 13 10:12:07 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_waldorf.pdf (Sat Jun 13 10:17:48 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_june2009_wilson.pdf (Sat Jun 13 10:40:20 2009) Linked to by: Oberwolfach Workshop, June 2009  Strings, Fields, Topology

oberwolfach_kahle.pdf (Thu Jun 11 16:54:02 2009)

oberwolfach_schick.pdf (Thu Jun 11 11:57:58 2009)

oberwolfach_wilson.pdf (Thu Jun 11 16:50:45 2009)

obunke.pdf (Sat Jun 13 09:36:12 2009)

pFoldCoveringOfCircle.png (Tue Jan 24 06:02:00 2017)

pFoldCoveringOfCircleB.png (Tue Jan 24 06:03:22 2017)

pdftest.pdf (Sat Jul 9 23:06:15 2011)

pdf_entry.gif (Wed Dec 3 21:10:43 2008)

pdficon_small.gif (Wed Dec 3 18:01:44 2008)

pgarr.svg (Sun Jun 12 11:54:03 2011)

pic.jpg (Fri Oct 9 06:34:14 2009)

quant2states.pdf (Wed Jan 14 17:27:42 2009) Linked to by: bibrane

relcatsmodelcatsqcatsinftycats.jpg (Thu Apr 28 21:02:54 2016)

rightadjoint.png (Sun Oct 4 19:11:25 2009)

schuergdeformation.pdf (Tue Dec 16 20:43:27 2014) Linked to by: derived deformation theory

sdDelta2.gif (Fri Sep 9 10:27:44 2016)

sdDelta2a.gif (Fri Sep 9 10:33:49 2016)

sdDelta2r.jpg (Fri Sep 9 10:40:48 2016) Linked to by: subdivision

separation.png (Sun Jul 26 01:05:56 2009)

singularsimplices.jpg (Thu Feb 18 07:14:56 2016)

special_law.jpg (Tue Jul 20 04:04:45 2010) Linked to by: Frobenius algebra

suspension.jpg (Sun Sep 6 04:00:04 2009) Linked to by: suspension

symmetric_frobenius_algebra_law.jpg (Tue Jul 20 04:02:45 2010) Linked to by: Frobenius algebra

talk1.pdf (Mon Jun 8 11:53:51 2009)

thetaFeynmanDiagramm.png (Tue Nov 17 04:10:06 2015)

thetaFeynmandiagram.png (Tue Nov 17 04:02:56 2015)

thincat.png (Tue Sep 27 02:49:31 2011)

thtencrisp.pdf (Thu Aug 15 04:31:15 2013)

thten.pdf (Tue Dec 23 04:45:48 2008) Linked to by: cubical set  exposition, category of cubes  exposition, pasting diagram

tick2.png (Mon Apr 27 17:07:49 2009)

tick3.png (Mon Apr 27 17:10:00 2009)

tick4.png (Mon Apr 27 17:13:44 2009)

tick6.png (Mon Apr 27 17:16:47 2009) Linked to by: geometric infinityfunction theory

tincan.png (Wed Jun 30 21:45:08 2010) Linked to by: Schur functor

topvs.png (Tue May 11 08:54:58 2010)

trefoil.gif (Sat Oct 2 11:33:44 2010)

trefoil.pdf (Sat Oct 2 11:45:21 2010)

trefoil.tiff (Sat Oct 2 11:38:59 2010)

turn.png (Sun May 24 13:07:14 2009) Linked to by: pivotal symbols

twotrefoils.pdf (Sat Oct 2 11:59:19 2010) Linked to by: bridge number

vanilla.print.css (Tue Apr 3 14:37:19 2012)

virtualdoublecategorycell.png (Sat Apr 10 04:52:20 2010) Linked to by: virtual double category

virtualdoublecategorycomposite.png (Sat Apr 10 04:56:17 2010) Linked to by: virtual double category

warsaw.gif (Fri Mar 20 23:53:05 2009) Linked to by: 2009 March changes

warsaw.pdf (Wed Feb 24 18:14:57 2010) Linked to by: Warsaw circle

whiskypic.jpg (Fri May 28 23:00:03 2010) Linked to by: whisky club

worldlineformalismoverview.jpg (Tue Nov 17 05:21:29 2015)

zigzag0bigger.png (Sun Mar 29 19:01:39 2009)

zigzag0.png (Sun Mar 29 02:22:05 2009)

zigzag1bigger.png (Sun Mar 29 19:02:03 2009)

zigzag1.png (Sun Mar 29 02:25:49 2009)
and