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)
To define the tangent space of a smooth manifold, one may equivalently use curves or derivations of the algebra of smooth functions. For more general smooth spaces, these are no longer equivalent.
The operational tangent space of a generalized smooth space (at some point ) is the space of derivations of the algebra of germs (at ) of smooth functions.
The alternative notion (using curves) is that of the kinematic tangent space.
Last revised on April 15, 2013 at 06:33:45. See the history of this page for a list of all contributions to it.