莫尔斯理论入门-教辅教材-文化科教-太极之巅书单号

书刊介绍

莫尔斯理论入门内容简介

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.

莫尔斯理论入门目录

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

莫尔斯理论入门节选

《莫尔斯理论入门》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.