Methods of differential geometry in algebraic topology

M. Karoubi, C. Leruste

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.

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[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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この本の情報

書名 Methods of differential geometry in algebraic topology
著作者等 Karoubi, Max
Leruste, Christian
Hitchin N.J.
Leruste C.
書名別名 Algebraic topology via differential geometry

Méthodes de géométrie différentielle en topologie algébrique
シリーズ名 London Mathematical Society lecture note series
出版元 Cambridge University Press
刊行年月 1987
ページ数 363 p.
大きさ 23 cm
ISBN 0521317142
NCID BA01338549
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言語 英語
原文言語 フランス語
出版国 イギリス
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