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)
In differential geometry the de Rham differential is the differential in the de Rham complex, “exterior derivative” acting on differential forms.
Let be a cohesive (∞,1)-topos and write for its tangent cohesive (∞,1)-topos.
Given a stable homotopy type cohesion provides two objects
which may be interpreted as de Rham complexes with coefficients in , the first one restricted to negative degree, the second to non-negative degree. Moreover, there is a canonical map
which interprets as the de Rham differential . See at differential cohomology diagram for details.
Last revised on May 3, 2023 at 05:00:03. See the history of this page for a list of all contributions to it.