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
(shape modality $\dashv$ flat modality $\dashv$ sharp modality)
$(\esh \dashv \flat \dashv \sharp )$
dR-shape modality$\dashv$ dR-flat modality
$\esh_{dR} \dashv \flat_{dR}$
(reduction modality $\dashv$ infinitesimal shape modality $\dashv$ infinitesimal flat modality)
$(\Re \dashv \Im \dashv \&)$
fermionic modality$\dashv$ bosonic modality $\dashv$ rheonomy modality
$(\rightrightarrows \dashv \rightsquigarrow \dashv Rh)$
Models
Models for Smooth Infinitesimal Analysis
smooth algebra ($C^\infty$-ring)
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
manifolds and cobordisms
cobordism theory, Introduction
Definitions
Genera and invariants
Classification
Theorems
A notion of infinite-dimensional manifold. A Banach manifold is a manifold modelled on Banach spaces. By default, transition maps are taken to be smooth.
Every paracompact Banach manifold is an absolute neighbourhood retract.
The category of smooth Banach manifolds has a full and faithful functor into the category of diffeological spaces. In terms of Chen smooth spaces this was observed in (Hain). For more see at Fréchet manifold – Relation to diffeological spaces.
For general references see at infinite-dimensional manifold.
Aspects of the homotopy theory of Banach manifolds:
The full subcategory embedding into the category of diffeological spaces:
Last revised on September 19, 2021 at 06:25:40. See the history of this page for a list of all contributions to it.