C^\infinity - Differentiable Spaces

2003
ISBN: 978-3-540-20072-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1824, 196 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 330 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Sancho de Salas, Juan B.

Navarro González, Juan A.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

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.