lSpace All pages

Overview

The lSpace wiki has 393 pages. Some of these are organised into categories.

Pages

• "Parallel" transport - revisited
• 18 Lectures on K-Theory
• A bicategory of reduced orbifolds from the point of view of differential geometry
• A bigroupoid's topology
• A bit of tropical geometry
• A bundle gerbe construction of a spinor bundle from the smooth free loop of a vector bundle
• A characterization of inner product spaces
• A combinatorial description of homotopy groups of spheres
• A Comment on the calculation of the Lie algebra cocycle in the book Loop Groups
• A comment on the construction of the maximal globally hyperbolic Cauchy development
• A comprehensive introduction to differential geometry. {V}ol. {I}
• A Construction of String 2-Group Models using a Transgression-Regression Technique
• A continuous deRham antidifferential
• A convenient category of supermanifolds
• A convenient setting for differential geometry and global analysis
• A convenient setting for differential geometry and global analysis. {II}
• A Functorial Map from Knots in Thickened Surfaces to Classical Knots and Generalisations of Parity
• A general context for Goodwillie Calculus
• A general theory of self-similarity
• A geometric construction of the Witten genus, II
• A geometric interpretation of the homotopy groups of the cobordism category
• A Geometric Model for Odd Differential K-theory
• A gerbe obstruction to quantization of fermions on odd dimensional manifolds with boundary
• A Khovanov homotopy type or two
• A Lie algebra for Fr\"olicher groups
• A loop group extension of the odd Chern character
• A Loop Space Formulation for Geometric Lifting Problems
• A model structure on the category of diffeological spaces
• A new look at connections
• A new topological invariant for the "Rubik's Magic" puzzle
• A non regular Fr\"olicher Lie group of diffeomorphisms
• A note on a diffeomorphism between two Banach spaces
• A note on bundle gerbes and infinite-dimensionality
• A note on jet and geometric approach to higher order connections
• A remark on distributions and the de Rham theorem
• A short exposition of the Madsen-Weiss theorem
• A Smooth Model for the String Group
• A Steenrod Square on Khovanov Homology
• A subtle new invariant for framed knots and links
• A survey of Heegaard Floer homology
• A topological introduction to knot contact homology
• A topological view of ordered groups
• A Tower Connecting Gauge Groups to String Topology
• A Whirlwind Tour of the World of $(\infty,1)$-categories
• A zoo of diffeomorphism groups on $\mathbb R^n$
• Abstract and concrete categories: the joy of cats
• Adequate subcategories
• Algebra+Homotopy=Operad
• Algebraic theories, monads, and arities
• Algebraic theories, span diagrams and commutative monoids in homotopy theory
• Almost complex 4-manifolds with vanishing first {C}hern class
• An Affine Index Polynomial Invariant of Virtual Knots
• An H-Principle With Boundary Condition
• An infinite family of convex Brunnian links in $R^n$
• An informal introduction to topos theory
• An introduction to C-infinity schemes and C-infinity algebraic geometry
• An introduction to d-manifolds and derived differential geometry
• An introduction to finite type invariants of knots and 3-manifolds
• An introduction to high dimensional knots
• An operad for splicing
• An upper bound on Reidemeister moves
• Andrew Stacey
• Around finite-dimensionality in functional analysis
• Aspherical manifolds that cannot be triangulated
• Axiomatic Differential Geometry 2-2: Differential Forms
• Axiomatic Differential Geometry I
• Axiomatic Differential Geometry II-3
• Axiomatic Differential Geometry III-1
• Axiomatic Differential Geometry III-2
• Axiomatic Differential Geometry III-3
• Axiomatic TQFT, Axiomatic DQFT, and Exotic 4-Manifolds
• Axioms for convenient calculus
• Backward lambda-lemma and Morse filtrations
• Balloons and Hoops and their Universal Finite Type Invariant, BF Theory, and an Ultimate Alexander Invariant
• Band surgeries and crossing changes between fibered links
• Basic results on braid groups
• Behavior of the Eilenberg-Moore spectral sequence in derived string topology
• Biring and plethory structures on integer-valued polynomial rings
• Bornoligies, Topological Games and Function Spaces
• Braid equivalences and the $L$--moves
• Bundles of spectra and algebraic K-theory
• Cartan decomposition for complex loop groups
• Cat\'egories cart\'esiennement ferm\'ees engendr\'ees par des mono\"\i des
• Categorification and applications in topology and representation theory
• Category Theory Using String Diagrams
• Central cohomology operations and K-theory
• Champs continus d'espaces hilbertiens et de {$C^{\ast} $}-alg\`ebres
• Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid
• Characteristic classes in $TMF$ of level 3
• Charged Spaces
• Chasing diagrams in cryptography
• Chern-Weil forms and abstract homotopy theory
• Chern-Weil theory for certain infinite-dimensional Lie groups
• Chiral differential operators: formal loop group actions and associated modules
• Circle actions and scalar curvature
• Circle actions, central extensions and string structures
• Classification of symmetry groups for planar n-body choreographies
• Clifford modules and invariants of quadratic forms
• Cobordism obstructions to independent vector fields
• Cohomology in electromagnetic modeling
• Compactifying String Topology
• Comparative Smootheology
• Completed power operations for Morava E-theory
• Configuration space integrals and the cohomology of the space of homotopy string links
• Configuration space integrals and the topology of knot and link spaces
• Configurations spaces and Theta_n
• Connections, path liftings and Ambrose-Singer theorem on diffeological bundles
• Continuity of bilinear maps on direct sums of topological vector spaces
• Continuity of discrete homomorphisms of diffeomorphism groups
• Controllability on infinite-dimensional manifolds
• Corrigendum: "On the Floer homology of cotangent bundles"
• Cosimplicial C-infinity rings and the de Rham complex of Euclidean space
• Curved String Topology and Tangential Fukaya Categories II
• Cylindrical model structures
• D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
• Dehn surgery on knots of wrapping number 2
• Deloops of the spaces of long embeddings
• Derived string topology and the Eilenberg-Moore spectral sequence
• Detecting and realising characteristic classes of manifold bundles
• Diffeologies, Differential Spaces, and Symplectic Geometry
• Diffeology
• Diffeomorphism groups of balls and spheres
• Differentiable mappings between spaces of sections
• Differentiable structures on metric measure spaces: A Primer
• Differentiable vectors and unitary representations of Frechet-Lie supergroups
• Differential calculus in locally convex spaces
• Differential cohomology
• Differential cohomology in a cohesive infinity-topos
• Differential Geometry of Microlinear Frolicher Spaces
• Differential Geometry of Microlinear Frolicher Spaces III
• Differential K-theory. A survey
• Differentiating Matrix Functions
• Discrete module categories and operations in K-theory
• Distributivity versus associativity in the homology theory of algebraic structures
• Edinburgh Lectures on Geometry, Analysis and Physics
• Einstein Manifolds and Extremal Kahler Metrics
• Enumerating lattices of subsets
• Equivalence of string and fusion loop-spin structures
• Equivariant calculus of functors and Z/2-analyticity of real K-theory
• Equivariant holonomy for bundles and abelian gerbes
• Equivariant principal bundles and their classifying spaces
• Equivariant, string and leading order characteristic classes associated to fibrations
• Existence of 'Darboux chart' on loop space
• Extension of {$C\sp{\infty }$} functions defined in a half space
• Fivebranes and Knots
• Formal Groups, Witt vectors and Free Probability
• Formal plethories
• Four Equivalent Versions of Non-Abelian Gerbes
• Fractions in elementary education
• Free loop space and homology
• Frobenius Pairs and Atiyah Duality
• From operator categories to topological operads
• Fréchet manifolds as diffeological spaces
• Functorial semantics of algebraic theories and some algebraic problems in the context of functorial semantics of algebraic theories
• Gauge and Integrable Theories in Loop Spaces
• Gauge theory and string topology
• Generalised Miller-Morita-Mumford classes for block bundles and topological bundles
• Generalized complex geometry and T-duality
• Geometric structure for the tangent bundle of direct limit manifolds
• Geometry of Bounded Frechet Manifolds
• Globalizing fibrations by schedules
• Graphic lambda calculus and knot diagrams
• Group actions on stacks and applications to equivariant string topology for stacks
• Groupes diff\'erentiels
• Groupoid Quantization of Loop Spaces
• Groups, cacti and framed little discs
• Hamiltonian BF theory and projected Borromean Rings
• Higher homotopy operations and André-Quillen cohomology
• Higher order Josephson effects
• Higher order {M}assey products and links
• Hitchhiker's guide to the fractional Sobolev spaces
• HomePage
• Homolog\'ia de Morse en variedades compactas
• Homological stability for spaces of surfaces
• Homological stability for unordered configuration spaces
• Homologies are infinitely complex
• Homology groups of filtrations
• Homomorphisms between diffeomorphism groups
• Homotopy automorphisms of R-module bundles, and the K-theory of string topology
• Homotopy Groups of Diagonal Complements
• Homotopy homomorphisms and the classifying space functor
• Homotopy theory of infinite dimensional manifolds
• Horizontal Path Lifting for General Connections
• Hyperbolic Geometry and Homotopic Homeomorphisms of Surfaces
• Identifying the Canonical Component for the Whitehead Link
• Induced differential forms on manifolds of functions
• Infinite dimensional manifolds from a new point of view
• Infinite-dimensional manifolds as ringed spaces
• Injectivity of satellite operators in knot concordance
• Intrinsic weak derivatives and Sobolev spaces between manifolds
• Introduction to Khovanov Homologies. II. Reduced Jones superpolynomials
• Introduction to Vassiliev Knot Invariants
• Introduction to Virtual Knot Theory
• Invariant tubular neighborhoods in infinite-dimensional {R}iemannian geometry, with applications to {Y}ang-{M}ills theory
• Invariants of Links in Thickened Surfaces
• Iterated integrals over higher dimensional loops
• JSJ-decompositions of knot and link complements in the 3-sphere
• Juggling braids and links
• K-Theories for Certain Infinite Rank Bundles
• Khovanov Homology
• Khovanov homology for virtual links using cobordisms
• Knot invariants and higher representation theory II: the categorification of quantum knot invariants
• Knot Polynomials: Myths and Reality
• La Grassmannienne non-linéaire comme variété fréchétique homogène
• Lectures on generalised cohomology
• Lectures on generalized geometry
• Lie-Hopf algebras and loop homology of suspension spaces
• Lifting Problems and Transgression for Non-Abelian Gerbes
• Linear spaces and differentiation theory
• Linear spaces and involutive duality functors
• Link groups
• Link invariants via counting surfaces
• Local invariant for scale structures on mapping spaces
• Local Theory for 2-Functors on Path 2-Groupoids
• Localisation and Completion with an addendum on the use of Brown-Peterson homology in stable homotopy
• Localisations of cobordism categories and invertible TFTs in dimension two
• Locally convex topological algebras of generalized functions: compactness and nuclearity in a nonlinear context
• Long exact sequences for de Rham cohomology of diffeological spaces
• Loop Differential K-theory
• Loop Groups, Higgs Fields and Generalised String Classes
• Loop-fusion cohomology and transgression
• Low Dimensional Topology and Ordering Groups
• Manifold calculus and homotopy sheaves
• Mapping spaces and R-completion
• Modeling Collaborations with Persistent Homology
• Models for $(\infty, n)$-categories and the cobordism hypothesis
• Modular Invariants and Twisted Equivariant K-theory II: Dynkin diagram symmetries
• Monads with arities and their associated theories
• Monoidal categories in, and linking, geometry and algebra
• Morse Homotopy and Homological Conformal Field Theory
• Multiplicative Structures on the Twisted K-theory over Finite Groups
• Non-abelian higher gauge theory and categorical bundle
• Nonlinear Generalized Functions: their origin, some developments and recent advances
• Notes on algebras and vector spaces of functions
• Notes on regularity properties of infinite-dimensional Lie groups
• Nuclear and trace ideals in tensored {$\ast$}-categories
• Of Sullivan models, Massey products, and twisted Pontrjagin products
• On 2-dimensional topological field theories
• On 2-Holonomy
• On a generalization of the notion of manifold
• On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$
• On homotopy Brunnian links and the kappa-invariant
• On Leonardo da Vinci's proof of the Theorem of Pythagoras
• On realizing diagrams of Pi-algebras
• On Structure and Organization: An Organizing Principle
• On the cohomology of the free loop space of a complex projective space
• On the colored Jones polynomials of ribbon links, boundary links and Brunnian links
• On the deformation of path algebras
• On the existence of bibundles
• On the Homology of Elementary Abelian Groups as Modules over the Steenrod Algebra
• On the rational homology of high dimensional analogues of spaces of long knots
• On the Smoothness of Functors
• On the string topology category of compact Lie groups
• On the topological contents of eta invariants
• On the topology of quasitopological fundamental groups
• On the Unicity of the Homotopy Theory of Higher Categories
• On Theories of Superalgebras of Differentiable Functions
• Operator calculus - the exterior differential complex
• Orbispaces and their Mapping Spaces via Groupoids: A Categorical Approach
• Overview of the Geometries of Shape Spaces and Diffeomorphism Groups
• Parallel Transport on Higher Loop Spaces
• Parallel Weighings
• Partitions of unity and coverings
• Path algebras and de Broglie waves
• Path space as manifold, manifold of maps, infinite dimensional manifold
• Patterns formed by coins
• Perturbative sigma models, elliptic cohomology and the Witten genus
• Picture-Hanging Puzzles
• Playing simple loony dots and boxes endgames optimally
• Polyfolds: A First and Second Look
• Pontryagin invariants and integral formulas for Milnor's triple linking number
• Positive definite metric spaces
• Positive definite superfunctions and unitary representations of Lie supergroups
• Positive energy representations and continuity of projective representations for general topological groups
• Power operations and coactions in highly commutative homology theories
• Principal bundles of embeddings and nonlinear Grassmannians
• Projective lines as groupoids with projection structure
• Properties of knots preserved by cabling
• Puzzling the 120-cell
• Quantum Knot Invariants
• Rational homotopy -- Sullivan models
• Reconfigurable knots and links in chiral nematic colloids
• Relations among characteristic classes of manifold bundles
• Relative Microlinearity -Towards the general theory of fiber bundles for Frolicher spaces
• Representations of derived A-infinity algebras
• Rethinking set theory
• Rho-classes, index theory and Stolz' positive scalar curvature sequence
• Satellite operators as group actions on knot concordance
• Segal's Spectral Sequence in Twisted Equivariant K-theory for proper and discrete actions
• Semicoverings: a generalization of covering space theory
• Singularities and Quinn spectra
• Skein relations for {M}ilnor's {[mu]}-invariants
• Smooth group representations on bornological vector spaces
• Smooth Manifolds vs Differential triads
• Smooth structures on non-orientable four-manifolds and free involutions
• Smooth, easy to compute interpolating splines
• SO(3) Homology of Graphs and Links
• Sobolev Metrics on Diffeomorphism Groups and the Derived Geometry of Spaces of Submanifolds
• Some problems in functional analysis inspired by Hahn Banach type theorems
• Some recent work in Frechet geometry
• Spin structures on loop spaces that characterize string manifolds
• Splitting Varieties for Triple Massey Products
• Stable real K-theory and real topological Hochschild homology
• Steenrod operations and the diagonal morphism
• Stochastic manifolds
• String geometry vs. spin geometry on loop spaces
• String structures and the path fibration of a group
• String topology and the based loop space
• String Topology, Euler Class and TNCZ free loop fibrations
• Strongly internal sets and generalized smooth functions
• Sub-riemannian geometry from intrinsic viewpoint
• Sub-Riemannian geometry on infinite-dimensional manifolds
• Supersymmetric field theories and generalized cohomology
• Tackling the Trefoils
• Talbot Workshop 2010 Talk 2: K-Theory and Index Theory
• Tame Fréchet submanifolds
• TCFT Elliptic Objects
• The (n)-solvable filtration of the link concordance group and Milnor's invariants
• The Alexander and Jones Polynomials Through Representations of Rook Algebras
• The blob complex
• The caloron correspondence and higher string classes for loop groups
• The Caloron Correspondence and Odd Differential K-theory
• The Chern Character of Certain Infinite Rank Bundles arising in Gauge Theory
• The Classification of Two-Dimensional Extended Topological Field Theories
• The Cleavage Operad and String Topology of Higher Dimension
• The cobordism hypothesis
• The cohomology of lambda-rings and K-theory
• The D-topology for diffeological spaces
• The Determinant Line Bundle for Fredholm Operators: Construction, Properties, and Classification
• The diffeomorphism group of a non-compact orbifold
• The fundamental group as topological group
• The Geometry of Orbifolds via Lie Groupoids
• The Gromoll filtration, KO-characteristic classes and metrics of positive scalar curvature
• The homotopy theory of diffeological spaces, I. Fibrant and cofibrant objects
• The homotopy theory of function spaces: A survey
• The homotopy theory of Khovanov homology
• The Index Bundle for a Family of Dirac-Ramond Operators
• The inverse function theorem of Nash and Moser
• The Kirby torus trick for surfaces
• The magnitude of a graph
• The magnitude of metric spaces
• The module structure of the equivariant K-theory of the based loop group of SU(2)
• The Moore-Penrose Pseudoinverse. A Tutorial Review of the Theory
• The near-Hopf ring structure on the integral cohomology of 1-connected Lie groups
• The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits
• The Orbit Space and Basic Forms of a Proper Lie Groupoid
• The Polygons of Albrecht Dürer -1525
• The product structure of the equivariant K-theory of the based loop group of SU(2)
• The realization space of a {[Pi]}-algebra: a moduli problem in algebraic topology
• The space of paths in complex projective space with real boundary conditions
• The Tangent Functor Monad and Foliations
• The theory and practice of Reedy categories
• The triangulation of manifolds
• The Trieste look at Knot Theory
• The Unitary Group In Its Strong Topology
• The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles
• The Yang-Mills Gradient Flow and Loop Groups
• Things to do with a broken stick
• Three approaches to Morse-Bott homology
• Three dimensions of knot coloring
• Tight spans, Isbell completions and semi-tropical modules
• Topics on nonlinear generalized functions
• Topological Aspects of Differential Chains
• Topological characterization of various types of rings of smooth functions
• Topological modular forms and conformal nets
• Topological Strings, D-Model, and Knot Contact Homology
• Topology and subsets - the story of a theorem
• Topology Explains Why Automobile Sunshades Fold Oddly
• Topology of Musical Data
• Torelli spaces of high-dimensional manifolds
• Transgression to Loop Spaces and its Inverse, III: Gerbes and Thin Fusion Bundles
• Triple gear
• Tubular configurations: equivariant scanning and splitting
• Tutorial on the braid groups
• Twisted $K$-theory
• Twisted K-theory and obstructions against positive scalar curvature metrics
• Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class
• Umkehr Maps Patched via the Compactified Cleavage Operad
• Unitary Representations of Unitary Groups
• Universal operations in Hochschild homology
• Unstable Adams operations on p-local compact groups
• Using boundaries to find smooth norms
• Vector bundles and the {K}\"unneth formula
• Vector fields on mapping spaces and a converse to the AKSZ construction
• Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions
• Weakly Smooth Structures in Gromov-Witten Theory
• What is... a G_2 manifold?
• When is the underlying space of an orbifold a topological manifold?
• Whitney categories and the Tangle Hypothesis
• Workshop on the homotopy theory of homotopy theories
• Yet More Smooth Mapping Spaces and Their Smoothly Local Properties
• Zredukowane homologie Khovanova
• {$G$}-{H}ilbert bundles