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
Euler-Lagrange equation, de Donder-Weyl formalism?,
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
∞-Lie theory (higher geometry)
Given a smooth manifold and a vector field on it, one defines a series of operators on spaces of differential forms, of functions, of vector fields and multivector fields. For functions (derivative of along an integral curve of ); as multivector fields and forms can not be compared in different points, one pullbacks or pushforwards them to be able to take a derivative.
For vector fields . If is a differential form on , the Lie derivative of along is the linearization of the pullback of along the flow induced by
Denote by be the graded derivation which is the contraction with a vector field . By Cartan's homotopy formula,
An introduction in the context of synthetic differential geometry is in
A gentle elementary introduction for mathematical physicists
.
Last revised on March 23, 2017 at 09:29:00. See the history of this page for a list of all contributions to it.