C-Differentiable Spaces

  • Authors
  • Juan A. Navarro González
  • Juan B. Sancho de Salas

Part of the Lecture Notes in Mathematics book series (LNM, volume 1824)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 1-5
  3. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 7-20
  4. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 21-38
  5. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 39-49
  6. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 51-56
  7. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 57-68
  8. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 69-77
  9. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 79-87
  10. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 89-97
  11. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 99-111
  12. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 113-125
  13. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 127-150
  14. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 151-179
  15. Juan A. Navarro González, Juan B. Sancho de Salas
    Pages 181-183
  16. Back Matter
    Pages 185-188

About this book

Introduction

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 C^\infinity-rings and C^\infinity-schemes, as well as in the framework of Spallek’s C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.

Keywords

algebra differebtiable algebras differentiable spaces differential geometry manifold

Bibliographic information

  • DOI https://doi.org/10.1007/b13465
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-20072-7
  • Online ISBN 978-3-540-39665-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book