Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics pdf epub mobi txt 电子书 下载 2026
- 数学
- 微分几何7
- 学术读物
- 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
具体描述
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.
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这是一本没有繁琐计算的微分几何极品好书，一不留神就把Atiyah-Singer指标定理给推倒了。
评分主丛联络的定义。主丛中垂直向量场是李导数，killing场，而其水平是形式有水平提升。Minkowski定理（几何数论）推广到外尔渐进公式，再推广到Minakshisundaram–Pleijel zeta zeta函数收集了关键的紧黎曼曲面的拉普拉斯特征值的信息。特例是高斯博内特公式和外尔热渐进公式
评分主丛联络的定义。主丛中垂直向量场是李导数，killing场，而其水平是形式有水平提升。Minkowski定理（几何数论）推广到外尔渐进公式，再推广到Minakshisundaram–Pleijel zeta zeta函数收集了关键的紧黎曼曲面的拉普拉斯特征值的信息。特例是高斯博内特公式和外尔热渐进公式
评分这是一本没有繁琐计算的微分几何极品好书，一不留神就把Atiyah-Singer指标定理给推倒了。
评分主丛联络的定义。主丛中垂直向量场是李导数，killing场，而其水平是形式有水平提升。Minkowski定理（几何数论）推广到外尔渐进公式，再推广到Minakshisundaram–Pleijel zeta zeta函数收集了关键的紧黎曼曲面的拉普拉斯特征值的信息。特例是高斯博内特公式和外尔热渐进公式
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