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)
vector bundle, 2-vector bundle, (∞,1)-vector bundle
real, complex/holomorphic, quaternionic
One way to define a connection on a vector bundle is as a principal connection of the -principal bundle that the vector bundle is an associated bundle to. Another is as a covariant derivative on the space of sections of the vector bundle.
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An exposition with an eye towards applications in gauge theory is in section 16.3 of
Last revised on April 17, 2023 at 10:56:10. See the history of this page for a list of all contributions to it.