莫尔斯理论入门

图书信息

书 名: 莫尔斯理论入门

作者：（美）尼古莱斯库

出版社：世界图书出版公司

出版时间： 2010-9-1

ISBN: 9787510027291

开本： 16开

定价: 35.00 元

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 assume 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

3applications

3.1 the cohomology of complex grassmannians

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