莫尔斯理论入门 [An Invitation to Morse Theory] epub pdf mobi txt 电子书 下载 2024

莫尔斯理论入门 [An Invitation to Morse Theory] epub pdf mobi txt 电子书 下载 2024

☆☆☆☆☆
简体网页||繁体网页



点击这里下载

莫尔斯理论入门 [An Invitation to Morse Theory] epub pdf mobi txt 电子书 下载 2024

类似图书 点击查看全场最低价

---

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.

莫尔斯理论入门 [An Invitation to Morse Theory] epub pdf mobi txt 电子书 下载 2024

莫尔斯理论入门 [An Invitation to Morse Theory] 下载 epub mobi pdf txt 电子书 2024

评分☆☆☆☆☆

莫尔斯

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☆☆☆☆☆

装13买来的书，但没读进去！

评分☆☆☆☆☆

在大地线上，各点的主曲率方向均与该点上曲面法线相合。它在圆球面上为大圆弧，在平面上就是直线。在大地测量中，通常用大地线来代替法截线，作为研究和计算椭球面上各种问题。测地线是在一个曲面上，每一点处测地曲率均为零的曲线。 曲面上非直线的曲线是测地线的充分必要条件是除了曲率为零的点以外，曲线的主法线重合于曲面的法线。

评分☆☆☆☆☆

装13买来的书，但没读进去！

评分☆☆☆☆☆

1.1 相关定理及推论

评分☆☆☆☆☆

封皮做工不咋，内容还是很好的

评分☆☆☆☆☆

1 三维空间中的曲面

评分☆☆☆☆☆

微分拓扑的一部分，看着长见识

类似图书 点击查看全场最低价