formal smooth manifold

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 $\mathbb{R}^n \times D$, where $\mathbb{R}^n$ is a Cartesian space and $D$ is an infinitesimally thickened point. Here $\mathbb{R}^n$ is the underlying reduced manifold.

Section I.17 and I.19 of

- Anders Kock,
*Synthetic Differential Geometry*, (pdf)

Formal smooth manifolds of the simple product form $X \times D$ in the category of smooth loci for $X$ an ordinary smooth manifold and $D$ and infinitesimal space have been considered in section 4 of

- Eduardo Dubuc,
*Sur les modeles de la geometrie differentielle synthetique*Cahiers de Topologie et Géométrie Différentielle Catégoriques, 20 no. 3 (1979), p. 231-279 (numdam).

For more on this see Cahiers topos

Revised on January 5, 2013 21:38:01
by Urs Schreiber
(89.204.138.93)