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)
manifolds and cobordisms
cobordism theory, Introduction
Definitions
Genera and invariants
Classification
Theorems
A manifold, possibly infinite-dimensional, is called a convenient manifold – implicitly meaning: convenient for differential geometry – if it is modeled on a convenient vector space.
One should note that this usage of the adjective ‘convenient’ is different to that in ‘convenient category’, for example of smooth spaces. In that case the category is convenient, whereas here the objects are convenient.
Together with convenient vector spaces, convenient manifods embed into the Cahier topos of synthetic differential smooth spaces. See at Cahiers topos for more on this.
A standard textbook reference is
A survey is for instance in the slides
Last revised on February 9, 2013 at 22:24:07. See the history of this page for a list of all contributions to it.