This entry is about smooth manifolds with infinitesimal thickenings. For “formal spaces” in the sense that their de Rham complex is a formal dg-algebra, see there.
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)
A formal smooth manifold is a smooth manifold equipped possibly with infinitesimal extension.
In the differential cohesion of synthetic differential infinity-groupoids these are the spaces locally isomorphic to , where is a Cartesian space and is an infinitesimally thickened point. Here is the underlying reduced manifold.
Anders Kock, Formal manifolds and synthetic theory of jet bundles, Cahiers de Topologie et Géométrie Différentielle Catégoriques (1980) Volume: 21, Issue: 3 (Numdam)
Anders Kock, section I.17 and I.19 of Synthetic Differential Geometry, (pdf)
Formal smooth manifolds of the simple product form in the category of smooth loci for an ordinary smooth manifold and and infinitesimal space have been considered in section 4 of
For more on this see Cahiers topos
Last revised on November 4, 2018 at 07:15:13. See the history of this page for a list of all contributions to it.