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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
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.
Bibliographic Information
Book Title: C^\infinity - Differentiable Spaces
Authors: Juan A. Navarro González, Juan B. Sancho de Salas
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b13465
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2003
Softcover ISBN: 978-3-540-20072-7Published: 29 October 2003
eBook ISBN: 978-3-540-39665-9Published: 09 December 2003
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVI, 196
Topics: Global Analysis and Analysis on Manifolds, Commutative Rings and Algebras