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Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics
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简体网页||繁体网页
John Roe 作者
Chapman & Hall/CRC
译者
1999-01-06 出版日期
209 页数
USD 93.95 价格
Paperback
丛书系列
9780582325029 图书编码

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 在线电子书 图书标签: 数学  微分几何7  学术读物  Pitman.Research.Notes.in.Math.  Physics   

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发表于2024-11-04

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Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024


Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 在线电子书 用户评价

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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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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☆☆☆☆☆

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☆☆☆☆☆

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

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 在线电子书 著者简介

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 在线电子书 图书目录

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 在线电子书 pdf 下载 txt下载 epub 下载 mobi 在线电子书下载

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition (Research Notes in Mathematics 在线电子书 图书描述

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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