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Lecture Notes in Mathematics

C^\infinity - Differentiable Spaces

Authors: Navarro González, Juan A., Sancho de Salas, Juan Bautista

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  • ISBN 978-3-540-39665-9
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About this book

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.

Table of contents (14 chapters)

Table of contents (14 chapters)
  • Introduction

    Pages 1-5

    Navarro González, Juan A. (et al.)

  • 1 Differentiable Manifolds

    Pages 7-20

    Navarro González, Juan A. (et al.)

  • 2 Differentiable Algebras

    Pages 21-38

    Navarro González, Juan A. (et al.)

  • 3 Differentiable Spaces

    Pages 39-49

    Navarro González, Juan A. (et al.)

  • 4 Topology of Differentiable Spaces

    Pages 51-56

    Navarro González, Juan A. (et al.)

Buy this book

eBook 28,88 €
price for Spain (gross)
  • ISBN 978-3-540-39665-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 36,35 €
price for Spain (gross)
  • ISBN 978-3-540-20072-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
C^\infinity - Differentiable Spaces
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1824
Copyright
2003
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-39665-9
DOI
10.1007/b13465
Softcover ISBN
978-3-540-20072-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVI, 196
Topics