The Morse-Witten complex via dynamical systems
arXiv:math/0411465 · doi:10.1016/j.exmath.2005.09.001
Abstract
Given a smooth closed manifold M, the Morse-Witten complex associated to a Morse function f and a Riemannian metric g on M consists of chain groups generated by the critical points of f and a boundary operator counting isolated flow lines of the negative gradient flow. Its homology reproduces singular homology of M. The geometric approach presented here was developed in [We-93] and is based on tools from hyperbolic dynamical systems. For instance, we apply the Grobman-Hartman theorem and the Lambda-Lemma (Inclination Lemma) to analyze compactness and define gluing for the moduli space of flow lines.
38 pages, 17 figures, minor modifications and corrections
References in corpus (1)
Cited by in corpus (13)
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