新华书店正版/示性类/(美)米尔纳

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基本信息

书名:示性类

原价：39.00元

作者:(美)米尔纳

出版社：世界图书出版公司

出版日期：2009-08-01

ISBN：9787510005336

字数：

页码：330

版次：1

装帧：平装

开本：24开

商品标识：bookuu1599751

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The theory of characteristic classes began in the year 1935 with almost simultaneous work by HASSLER WHITNEY in the United States and EDUARD STIEFEL in Switzerland.Stiefel's thesis, written under the direction of Heinz Hopf, introduced and studied certain "characteristic"homology classes determined by the tangent bundle of a smooth manifold.Whitney, then at Harvard University, treated the case of an arbitrary sphere bundle. Somewhat later he invented the language of cohomology theory,hence the concept of a characteristic cohomology class, and proved the basic product theorem.

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Preface
§1. Smooth Manifolds
§2. Vector Bundles
§3. Constructing New Vector Bundles Out of Old
§4. Stiefel-Whitney Classes
§5. Grassmann Manifolds and Universal Bundles
§6. A Cell Structure for Grassmann Manifolds
§7. The Cohomology Ring H*(Gn; Z/2)
§8. Existence of Stiefel-Whitney Classes
§9. Oriented Bundles and the Euler Class
§10. The Thorn Isomorphism Theorem
§11. Computations in a Smooth Manifold
§12. Obstructions
§13. Complex Vector Bundles and Complex Manifolds
§14. Chern Classes
§15. Pontrjagin Classes
§16. Chern Numbers and Pontrjagin Numbers
§17. The Oriented Cobordism Ring Ω*
§18. Thorn Spaces and Transversality
§19. Multiplicative Sequences and the Signature Theorem
§20. Combinatorial Pontrjagin Classes
Epilogue
Appendix A: Singular Homology and Cohomology
Appendix B: Bernoulli Numbers
Appendix C: Connections, Curvature, and Characteristic Classes.
Bibliography
Index