Methods of differential geometry in algebraic topology
著者
書誌事項
Methods of differential geometry in algebraic topology
（London Mathematical Society lecture note series, 99）
Cambridge University Press, 1987
- タイトル別名
-
Méthodes de géométrie différentielle en topologie algébrique
Algebraic topology via differential geometry
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注記
Translation of: Métodes de géométrie différentielle en topologie algébrique
Includes index
内容説明・目次
内容説明
In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.
目次
- Introduction
- 1. Algebraic preliminaries
- 2. differential forms on an open subset of Rn
- 3. differentiable manifolds
- 4. De Rham cohomology of differentiable manifolds
- 5. Computing cohomology
- 6. Poincare duality - Lefschetz' theorem
- Appendixes
- Bibliography
- Index.
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