Introduction To Differential Manifolds, An
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A01=Charles B Thomas
A01=Dennis Barden
Author_Charles B Thomas
Author_Dennis Barden
Category=PBMP
Category=PBP
De Rham Cohomology
Degrees and Indices
Differential Manifolds
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Fibre Bundles
Product details
- ISBN 9781860943553
- Publication Date: 13 Mar 2003
- Publisher: Imperial College Press
- Publication City/Country: GB
- Product Form: Paperback
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This invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology. Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincaré-Hopf theorem relating the Euler number of a manifold and the index of a vector field. Each chapter contains exercises of varying difficulty for which solutions are provided. Special features include examples drawn from geometric manifolds in dimension 3 and Brieskorn varieties in dimensions 5 and 7, as well as detailed calculations for the cohomology groups of spheres and tori.
