莫尔斯理论入门
2010-9
世界图书出版公司
尼古莱斯库
241
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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.
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 complex morse theory
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学习morse理论的不错入门书
很好的莫尔斯理论入门书。
这是全英文的。。。
如题，那本是经典，比较短小精悍，再看这本收获更多