莫尔斯理论入门 [An Invitation to Morse Theory] pdf epub mobi txt 电子书 下载 2025

简体网页||繁体网页

☆☆☆☆☆

[美] 尼古莱斯库 著

出版社： 世界图书出版公司

ISBN：9787510027291

版次：1

商品编码：10762448

包装：平装

外文名称：An Invitation to Morse Theory

开本：24开

出版时间：2010-09-01

用纸：胶版纸

页数：241

正文语种：英文

内容简介

As the the title suggests， the goal of this book is to give the reader a taste of the “unreasonable effectiveness” of Morse theory. The main idea behind thistechnique can be easily visualized.
Suppose M is a smooth， compact manifold， which for simplicity we as-sume is embedded in a Euclidean space E. We would like to understand basictopological invariants of M such as its homology， and we attempt a “slicing” technique.

目录

Preface
Notations and conventions
1 Morse Functions
1.1 The Local Structure of Morse Functions
1.2 Existence of Morse Functions

2 The Topology of Morse Functions
2.1 Surgery，Handle Attachment.and Cobordisms
2.2 The Topology of Sublevel Sets
2.3 Morse Inequalities
2.4 Morse-Smale Dynamics
2.5 Morse-Floer Homology
2.6 Morse-Bott Functions
2.7 Min-Max Theory

3 Applications
3.1 The Cohomology of Complex Grassmannians
3.2 Lefschetz Hyperplane Theorem
3.3 Symplectic Manifolds and Hamiltonian Flows
3.4 Morse Theory of Moment Maps
3.5 S1-Equivariant Localization

4 Basics of Comple X Morse Theory
4.1 Some Fundamental Constructions
4.2 Topological Applications of Lefschetz Pencils
4.3 The Hard Lefschetz Theorem
4.4 Vanishing Cycles and Local Monodromy
4.5 Proofofthe Picard Lefschetz formula
4.6 Global Picard-Lefschetz Formulae

5 Exercises and Solutions
5.1 Exercises
5.2 Solutions to Selected Exercises
References
Index

前言/序言

　　As the the title suggests， the goal of this book is to give the reader a taste of the “unreasonable effectiveness” of Morse theory. The main idea behind thistechnique can be easily visualized.
　　Suppose M is a smooth， compact manifold， which for simplicity we as-sume is embedded in a Euclidean space E. We would like to understand basictopological invariants of M such as its homology， and we attempt a “slicing” technique.
　　We fix a unit vector u in E and we start slicing M with the family of hyperplanes perpendicular to u. Such a hyperplane will in general intersectM along a submanifold （slice）. The manifold can be recovered by continuouslystacking the slices on top of each other in the same order as they were cut out of M.
　　Think of the collection of slices as a deck of cards of various shapes. If welet these slices continuously pile up in the order they were produced， we noticean increasing stack of slices. As this stack grows， we observe that there aremoments of time when its shape suffers a qualitative change. Morse theoryis about extracting quantifiable information by studying the evolution of theshape of this growing stack of slices.

评分☆☆☆☆☆

莫尔斯理论

评分☆☆☆☆☆

评分☆☆☆☆☆

微分拓扑学中利用微分流形上仅具非退化临界点的实值可微函数(称为莫尔斯函数)研究所给流形性质

评分☆☆☆☆☆

1.1 相关定理及推论

评分☆☆☆☆☆

2.1 唯一性及存在性

评分☆☆☆☆☆

1 三维空间中的曲面

评分☆☆☆☆☆

2 微分几何的测地线

评分☆☆☆☆☆

2.1 唯一性及存在性

评分☆☆☆☆☆

老板指定的书，不错，纸质很好，内容很好，适合研究生