| 词条 | 示性类 |
| 释义 | 图书信息出版社: 世界图书出版公司; 第1版 (2009年8月1日) 外文书名: Characteristic Classes 平装: 330页 正文语种: 英语 开本: 32 ISBN: 9787510005336, 7510005337 条形码: 9787510005336 尺寸: 22.4 x 15 x 1.4 cm 重量: 440 g 作者简介作者：(美国)米尔纳 内容简介《示性类》内容简介：The text which follows is based mostly on lectures at PrincetonUniversity in 1957. The senior author wishes to apologize for the delayin publication.The theory of characteristic classes began in the year 1935 with almostsimultaneous work by HASSLER WHITNEY in the United States andEDUARD STIEFEL in Switzerland. StiefeI's thesis, written under thedirection 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 spherebundle. Somewhat later he invented the language of cohomology theory,hence the concept of a characteristic cohomology class, and proved thebasic product theorem. 目录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 |
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