Backround
Definition
Presentation over a site
Models
synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
superalgebra and (synthetic ) supergeometry
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
The (∞,1)-topos of synthetic differential super -groupoids combines the properties of that of
Let CartSp be the site which is the full subcategory of that of formal duals of smooth superalgebras on those of the form
where
is the Cartesian space of dimension ;
is the super vector space of dimension ( is the odd line);
If here is the formal dual of the Artin algebra on commuting nilpotent elements, then such an object is written in (Konechny-Schwarz).
Let then
be the (∞,1)-category of (∞,1)-sheaves over this site.
Anatoly Konechny and Albert Schwarz,
On -dimensional supermanifolds in Supersymmetry and Quantum Field Theory (Dmitry Volkov memorial volume) Springer-Verlag (1998) Lecture Notes in Physics, 509 , J. Wess and V. Akulov (editors)(arXiv:hep-th/9706003)
Theory of -dimensional supermanifolds Sel. math., New ser. 6 (2000) 471 - 486
Urs Schreiber, section 4.5 of: differential cohomology in a cohesive topos
Hisham Sati, Urs Schreiber, Section 3.1.3 of: Proper Orbifold Cohomology (arXiv:2008.01101)
Urs Schreiber, Introduction to Higher Supergeometry, lecture at Higher Structures in M-Theory 2018, Durham Symposium
published in parts as: Higher Structures in M-Theory (with Branislav Jurčo, Christian Saemann, Martin Wolf), Fortschritte der Physik (2019) (arXiv:1903.02807, doi:10.1002/prop.201910001)
Last revised on October 2, 2020 at 07:23:46. See the history of this page for a list of all contributions to it.