The Morse-Witten complex via dynamical systems

Details The Morse-Witten complex via dynamical systems The Morse-Witten complex via dynamical systems

2004-11-21

arxiv.org/abs/math/0411465v2

Mathematics

Geometric Topology

38 pages, 17 figures, minor modifications and corrections

Scientific paper

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.

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