C^/infinity - Differentiable Spaces - Juan A. Navarro González, Juan B. Sancho de Salas

C^/infinity - Differentiable Spaces

Buch | Softcover
XVI, 196 Seiten
2003 | 2003
Springer Berlin (Verlag)
978-3-540-20072-7 (ISBN)
37,40 inkl. MwSt

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.

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.

Erscheint lt. Verlag 29.10.2003
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo XVI, 196 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 340 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Schlagworte 58A40, 58A05, 13J99 • Algebra • differebtiable algebras • differentiable spaces • Differentialgeometrie • Differential Geometry • Differenzialgeometrie • manifold
ISBN-10 3-540-20072-X / 354020072X
ISBN-13 978-3-540-20072-7 / 9783540200727
Zustand Neuware
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