Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics pdf epub mobi txt 電子書 下載2026
- 數學
- 微分幾何7
- 學術讀物
- Pitman.Research.Notes.in.Math.
- Physics
- Elliptic Operators
- Partial Differential Equations
- Topology
- Asymptotic Methods
- Functional Analysis
- Mathematical Analysis
- Differential Geometry
- Spectral Theory
- Operator Theory
- Research Notes in Mathematics
具體描述
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.
作者簡介
目錄資訊
讀後感
用戶評價
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
评分主叢聯絡的定義。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
评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。
评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。
评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。
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