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

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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.）

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.）

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

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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！

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本書作者是菲爾茲奬和沃爾夫將雙奬的獲得者，在拓撲學、幾何學等分支成就卓著。本書講解瞭從惠特尼到龐特裏亞金再到陳省身等人的示性類方麵的結果與成就，是一本難得的示性類方麵的著作。

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