C^\infinity - Differentiable Spaces / Edition 1

by Juan A. Navarro Gonzïlez, Juan B. Sancho de Salas

Overview

The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of Csub\infinity-rings and Csub\infinity-schemes, as well as in the framework of Spallek’s Csub\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.

Product Details

ISBN-13:	9783540200727
Publisher:	Springer Berlin Heidelberg
Publication date:	01/12/2004
Series:	Lecture Notes in Mathematics , #1824
Edition description:	2003
Pages:	196
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

Introduction.- 1. Differentiable Manifolds.- 2. Differentiable Algebras.- 3. Differentiable Spaces.- 4. Topology of Differentiable Spaces.- 5. Embeddings.- 6. Topological Tensor Products.- 7. Fibred Products.- 8. Topological Localization.- 9. Finite Morphisms.- 10. Smooth Morphisms.- 11. Quotients by Compact Lie Groups.- A. Sheaves of Fréchet Modules.- B. Space of Jets.- References.- Index.