示性类 [Characteristic Classes] epub pdf mobi txt 电子书 下载 2024

示性类 [Characteristic Classes] epub pdf mobi txt 电子书 下载 2024

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示性类 [Characteristic Classes] epub pdf mobi txt 电子书 下载 2024

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In 1942 LEV PONTRJAGIN of Moscow University began to study thehomology of Grassmann manifolds， using a cell subdivision due to CharlesEhresmann. This enabled him to construct important new characteristicclasses. （Pontrjagins many contributions to mathematics are the moreremarkable in that he is totally blind， having lost his eyesight in an acci-dent at the age of fourteen.）

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. StiefeIs 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.

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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

前言/序言

　　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. StiefeIs 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.
　　In 1942 LEV PONTRJAGIN of Moscow University began to study thehomology of Grassmann manifolds， using a cell subdivision due to CharlesEhresmann. This enabled him to construct important new characteristicclasses. （Pontrjagins many contributions to mathematics are the moreremarkable in that he is totally blind， having lost his eyesight in an acci-dent at the age of fourteen.）

示性类 [Characteristic Classes] epub pdf mobi txt 电子书 下载 2024

示性类 [Characteristic Classes] 下载 epub mobi pdf txt 电子书 2024

评分☆☆☆☆☆

非常棒，经典著作，值得购买！

评分☆☆☆☆☆

页面介绍和送过来的书封面不一样！？书本身是好书！

评分☆☆☆☆☆

米尔诺的书当然没的说，塞尔对其评价很高，他的数学写作有一种美感！

评分☆☆☆☆☆

很经典的一本书，值得购买

评分☆☆☆☆☆

里面有我想知道的东西，还没看不知道讲得怎样，不过Springer的书都不错

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好

评分☆☆☆☆☆

别的网站缺货了，只有京东有货，配送也非常快。

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愿你走出半生，归来仍是少年

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本书作者是菲尔兹奖和沃尔夫将双奖的获得者，在拓扑学、几何学等分支成就卓著。本书讲解了从惠特尼到庞特里亚金再到陈省身等人的示性类方面的结果与成就，是一本难得的示性类方面的著作。

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