圖書標籤: 數學 幾何 Geometry 物理 微分幾何7 馬上要看1 自鏇幾何 美國
发表于2024-12-23
Spin Geometry pdf epub mobi txt 電子書 下載 2024
This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.
對目前的我來說太難瞭點,沒讀懂多少。要求是Artin級彆的抽象代數,還得知道點微分幾何,一路到指標定理。發現一旦涉及錶示論我腦子就不怎麼轉瞭…
評分比起黎曼幾何,這書裏的內容對於現代數學要顯得重要的多,是為瞭介紹指標定理,卻也不盡限於此,從Clifford代數開始,K-theory 和 Soblev空間的一係列理論都講得很好,主要是講解的這些工具性的內容最後為指標定理的證明都起瞭作用,比起單獨的去念這些理論,這種方式無疑要有趣也有用的多
評分比起黎曼幾何,這書裏的內容對於現代數學要顯得重要的多,是為瞭介紹指標定理,卻也不盡限於此,從Clifford代數開始,K-theory 和 Soblev空間的一係列理論都講得很好,主要是講解的這些工具性的內容最後為指標定理的證明都起瞭作用,比起單獨的去念這些理論,這種方式無疑要有趣也有用的多
評分對目前的我來說太難瞭點,沒讀懂多少。要求是Artin級彆的抽象代數,還得知道點微分幾何,一路到指標定理。發現一旦涉及錶示論我腦子就不怎麼轉瞭…
評分對目前的我來說太難瞭點,沒讀懂多少。要求是Artin級彆的抽象代數,還得知道點微分幾何,一路到指標定理。發現一旦涉及錶示論我腦子就不怎麼轉瞭…
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Spin Geometry pdf epub mobi txt 電子書 下載 2024