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商品詳細
From Calculus to Cohomology : De Rham Cohomology and Characteristic Classes.
・ISBN 978-0-521-58956-7 paper GB£ 55.00
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| 著者・編者 | Madsen, Ib H. / Tornehave, Jxrgen, |
|---|---|
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 1997 |
| ページ数 | 296 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-9457＞ |
解説
De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last eleven chapters include Morse theory, index of vector fields, Poincare duality, vector bundles, connections and curvature, and the book ends with the general Gauss-Bonnet theorem. The text includes well over 150 exercises, and gives the background to the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology. It will be invaluable to anyone studying cohomology, curvature, and their applications.