点击选择搜索分类
首页 - 人类学- 正文
☆☆☆☆☆
||
[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
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.
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
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] 电子书 下载 mobi epub pdf txt
莫尔斯理论入门 [An Invitation to Morse Theory]-so88
莫尔斯理论入门 [An Invitation to Morse Theory] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[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
PrefaceNotations 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] 电子书 下载 mobi epub pdf txt
电子书下载地址:
相关电子书推荐:
- 文件名
- 阿司匹林传奇
- K线攻略之通道绝技—K线攻略实战技法 9787545405491
- 奇妙大自然-听爸爸讲科普-(低幼版)
- 一本书看透IPO A股IPO全流程深度剖析 沈春晖A股上市操作实务流程解析书籍 财务审核资本运作预售
- 世界科普巨匠经典译丛:十个为什么
- 不整脈治療のthe Basics 臨床に役立つ電気生理学
- 舌尖上的丁香——中国的外来植物 香料 9787553507026 姚欢远-RT
- 学习的革命 太平人寿TOP2000培训文字实录 郑荣禄博士十期培训主题报告文稿 寿险行业学习型组织真
- {RT}探索生命的奥秘-《科学传奇:探索人体的奥秘》编委会著 西南交通大学出版社 9787
- 猫のダヤンふせんbook わちふぃーるど
- 地球上的 动植物 黄宇,王元媛
- 趋势交易法(第三版)
- 满58包邮 鸟国拾趣 上 9787503882814 谈宜斌 中国林业出版社
- 正版 中国特色酒收藏投资指南(陈年酒投资的新风向,同《陈年白酒》、《地方名酒》构架中国酒投
- 研究生教材 电力市场经济学:理论与政策 中国电力出版社