莫爾斯理論入門

內(nèi)容概要

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.

書籍目錄

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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