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Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 2024 pdf epub mobi 電子書下載

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Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. The author builds towards proof of the Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics addressed include Hodge theory, Weyl's theorem on the distribution of the eigenvalues of the Laplacian, the asymptotic expansion for the heat kernel, and the index theorem for Dirac-type operators using Getzler's direct method. As a "dessert," the final two chapters offer discussion of Witten's analytic approach to the Morse inequalities and the L2-index theorem of Atiyah for Galois coverings. The text assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, Elliptic Operators, Topology, and Asymptotic Methods becomes the ideal vehicle for self-study or coursework. Mathematicians, researchers, and physicists working with index theory or supersymmetry will find it a concise but wide-ranging introduction to this important and intriguing field.

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 2024 pdf epub mobi 電子書下載

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發表於2024-11-23

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 2024 pdf epub mobi 電子書下載

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 2024 pdf epub mobi 電子書下載

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 2024 pdf epub mobi 電子書下載

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出版者:Chapman & Hall/CRC

作者:John Roe

出品人:

頁數:209

譯者:

出版時間:1999-01-06

價格:USD 93.95

裝幀:Paperback

isbn號碼:9780582325029

叢書系列:

圖書標籤: 數學微分幾何7 學術讀物 Pitman.Research.Notes.in.Math. Physics

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 2024 pdf epub mobi 電子書下載

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Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics pdf epub mobi 用戶評價

評分☆☆☆☆☆

這是一本沒有繁瑣計算的微分幾何極品好書，一不留神就把Atiyah-Singer指標定理給推倒瞭。

評分☆☆☆☆☆

這是一本沒有繁瑣計算的微分幾何極品好書，一不留神就把Atiyah-Singer指標定理給推倒瞭。

評分☆☆☆☆☆

主叢聯絡的定義。主叢中垂直嚮量場是李導數，killing場，而其水平是形式有水平提升。Minkowski定理（幾何數論）推廣到外爾漸進公式，再推廣到Minakshisundaram–Pleijel zeta zeta函數收集瞭關鍵的緊黎曼麯麵的拉普拉斯特徵值的信息。特例是高斯博內特公式和外爾熱漸進公式

評分☆☆☆☆☆

主叢聯絡的定義。主叢中垂直嚮量場是李導數，killing場，而其水平是形式有水平提升。Minkowski定理（幾何數論）推廣到外爾漸進公式，再推廣到Minakshisundaram–Pleijel zeta zeta函數收集瞭關鍵的緊黎曼麯麵的拉普拉斯特徵值的信息。特例是高斯博內特公式和外爾熱漸進公式

評分☆☆☆☆☆

這是一本沒有繁瑣計算的微分幾何極品好書，一不留神就把Atiyah-Singer指標定理給推倒瞭。

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 2024 pdf epub mobi 電子書下載

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