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synthetic differential supergeometry

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Context

Super-Geometry

superalgebra

and

supergeometry

Formal context

Superalgebra

Supergeometry

Structures

Applications

Synthetic differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

Theorems

Applications

Contents

Idea

Synthetic differential supergeometry pairs the concepts of

with those of

References

  • H. Nishimura, Synthetic differential supergeometry, International Journal of Theoretical Physics, Volume 37, Number 11 (1998) (journal)

  • David Yetter, Models for synthetic supergeometry, Cahiers, 29, 2 (1988) (NUMDAM)

  • H. Nishimura, Differential forms in synthetic differential supergeometry, International Journal of Theoretical Physics, Volume 38, Number 2 / Februar 1999 (journal)

  • H. Nishimura, Supersmooth topoi, International Journal of Theoretical Physics, Volume 39, Number 5 (journal)

  • H. Nishimura, Synthetic theory of superconnections, International Journal of Theoretical Physics, 39 (journal)

The article

  • Anatoly Konechny, Albert Schwarz, Theory of (k⊕l∣q)-dimensional supermanifolds Sel. math., New ser. 6 (2000) 471 { 486

considers manifolds with odd and even nilpotent functions: formal supermanifolds.

Revised on April 21, 2011 09:27:16 by Urs Schreiber (131.211.239.38)
Edit | Back in time (7 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: integration over supermanifolds, NQ-supermanifold, odd line, differentiable stack, Diff, smooth infinity-groupoid, smooth algebra, CartSp, differential geometry, Klein 2-geometry, superdifferential form, smooth Lorentzian space, generalized complex geometry, supermanifold, diffeological space, synthetic differential geometry, Lie group, smooth space, diffeomorphism, exterior algebra, tangent bundle, Models for Smooth Infinitesimal Analysis, differential forms in synthetic differential geometry, superconnection, diffiety, cartesian space, infinitesimal object, infinitesimal singular simplicial complex, Chevalley-Eilenberg algebra in synthetic differential geometry, supergeometry - contents, Riemannian manifold, de Rham space, de Rham theorem, (1,1)-dimensional Euclidean field theories and K-theory, (2,1)-dimensional Euclidean field theories and tmf, supergroup, isometry, (2,1)-dimensional Euclidean field theory, super vector space, super algebra, super Lie algebra, super vector bundle, Clifford algebra, D'Auria-Fre formulation of supergravity, supergravity, super Poincare Lie algebra, supergravity Lie 3-algebra, Supergravity and Superstrings - A Geometric Perspective, synthetic differential supergeometry, smooth topos, Kock-Lawvere axiom, amazing right adjoint, Euclidean geometry, supergeometry, supersymmetry, microlinear space, integration axiom, synthetic differential geometry - contents, smooth locus, Tietze extension theorem, lined topos, infinitesimal interval object, super smooth topos, Poincare group, Christoffel symbols, Riemannian metric, vector field, Levi-Civita connection, pseudo-Riemannian manifold, Riemannian geometry, shifted tangent bundle, Fermat theory, smooth loop space, smooth natural numbers, geodesic, differentiable map, Hadamard lemma, tubular neighbourhood, division algebra and supersymmetry, supersymmetric quantum mechanics, jet space, geodesic flow, Hodge star operator, Klein geometry, Cartan geometry, normal bundle, manifold structure of mapping spaces, smooth manifold, smooth map, variational calculus, volume form, Poincare lemma, Cahiers topos, Pfaffian line bundle, Lie derivative, Killing vector field, submersion, infinity-Lie group, Berezin integral, bundle 2-gerbe, ball, vielbein, gravitino, SCFT, infinitesimally thickened point, super infinity-groupoid, Stokes theorem, coisotropic submanifold, differentiation, chain rule, Steenrod-Wockel approximation theorem, superpoint, Green-Schwarz action functional, symmetric space, gerbe (in differential geometry), superparticle, Jacobian, Tannaka duality for Lie groupoids, smooth infinity-groupoid -- structures, D-scheme, Boman's theorem, super-groupoid, synthetic differential infinity-groupoid, diffeomorphism group, super L-infinity algebra, smooth super infinity-groupoid, formal smooth manifold, jet bundle, complex manifold, critical point, complex structure, local diffeomorphism, fermionic path integral, timelike curve, concrete smooth infinity-groupoid, orthogonal structure, C-infinity topology, infinite dimensional manifold, Borel's theorem, Cauchy surface, Killing vector, supersymmetry and Calabi-Yau manifolds, Killing spinor, torsion of a metric connection, 4-dimensional supergravity, higher Klein geometry, gradient flow, contents of contents, moduli space of Riemannian metrics, isometry group, Killing-Yano tensor, 3-dimensional supergravity, moment of inertia, Ricci flow, Morse homology, gradient, bivector, angular velocity, Euler-Arnold equation, symbol map, super-translation group, divergence, curl, on the manifold structure of singular loops, Killing tensor, 7-dimensional supergravity, gauged supergravity, derived differential geometry, exceptional generalized geometry, super parallel transport, bump function, type II supergravity, immersion of smooth manifolds