nLab
formal smooth manifold

Context

Synthetic differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

Theorems

Applications

Contents

Idea

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

References

  • 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 X×DX \times D in the category of smooth loci for XX an ordinary smooth manifold and DD 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 May 13, 2015 12:02:30 by Urs Schreiber (195.113.30.252)