| C^\Infinity - Differentiable Spaces 2003 Edition Contributor(s): Navarro González, Juan A. (Author), Sancho de Salas, Juan B. (Author) |
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ISBN: 354020072X ISBN-13: 9783540200727 Publisher: Springer OUR PRICE: $47.45 Product Type: Paperback Published: October 2003 |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Geometry - Differential - Mathematics | Algebra - General |
| Dewey: 516.36 |
| LCCN: 2003066694 |
| Series: Lecture Notes in Mathematics |
| Physical Information: 0.45" H x 6.14" W x 9.21" (0.67 lbs) 196 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 Fr?chet 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 Fr?chet spaces. |