示性類 [Characteristic Classes] 下載 mobi epub pdf 電子書 2025

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☆☆☆☆☆

[美] 米爾納 著

齣版社： 世界圖書齣版公司

ISBN：9787510005336

版次：1

商品編碼：10104511

包裝：平裝

外文名稱：Characteristic Classes

開本：24開

齣版時間：2012-06-01

用紙：膠版紙

頁數：330

正文語種：英語

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.）

評分☆☆☆☆☆

收到的書是白色封皮的。

評分☆☆☆☆☆

米爾諾的書當然沒的說，塞爾對其評價很高，他的數學寫作有一種美感！

評分☆☆☆☆☆

很經典的一本書，值得購買

評分☆☆☆☆☆

內容質量沒得說！

評分☆☆☆☆☆

很經典的一本書，值得購買

評分☆☆☆☆☆

願你走齣半生，歸來仍是少年

評分☆☆☆☆☆

很經典的一本書，值得購買

評分☆☆☆☆☆

這本書還是不錯的，需要注意的是照片與實際有點不符，是白色封麵的。優惠期間購買更實惠。

評分☆☆☆☆☆

這本書還是不錯的，需要注意的是照片與實際有點不符，是白色封麵的。優惠期間購買更實惠。