示性類 [Characteristic Classes] pdf epub mobi txt 电子书 下载 2025

☆☆☆☆☆

[美] 米爾納 著

圖書標籤:

• 拓撲學
• 代數拓撲
• 示性類
• 同調論
• 縴維叢
• 微分幾何
• 數學
• 高等數學
• 抽象代數
• 幾何學

出版社： 世界图书出版公司

ISBN：9787510005336

版次：1

商品编码：10104511

包装：平装

外文名称：Characteristic Classes

开本：24开

出版时间：2012-06-01

用纸：胶版纸

页数：330

正文语种：英语

編輯推薦

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.）

內容簡介

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.

內頁插圖

目錄

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.）

评分☆☆☆☆☆

好

评分☆☆☆☆☆

很经典的一本书，值得购买

评分☆☆☆☆☆

还没看过不发表内容的评论了，评论一下别的：纸张光滑，比世图出版的别的书要好很多，封面与图示不符，为白色红边，不过依然很漂亮，里面印刷不错。

评分☆☆☆☆☆

好

评分☆☆☆☆☆

别的网站缺货了，只有京东有货，配送也非常快。

评分☆☆☆☆☆

这本书还是不错的，需要注意的是照片与实际有点不符，是白色封面的。优惠期间购买更实惠。

评分☆☆☆☆☆

内容质量没得说！

评分☆☆☆☆☆

还没看过不发表内容的评论了，评论一下别的：纸张光滑，比世图出版的别的书要好很多，封面与图示不符，为白色红边，不过依然很漂亮，里面印刷不错。

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