The Morse-Witten complex via dynamical systems
نویسنده
چکیده
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 ofM . 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 λ-lemma (Inclination Lemma) to analyze compactness and define gluing for the moduli space of flow lines.
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تاریخ انتشار 2004