The Morse-Witten complex via dynamical systems
Geometric Topology
2014-02-10 v2 Dynamical Systems
Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.math/0411465,
title = {The Morse-Witten complex via dynamical systems},
author = {Joa Weber},
journal= {arXiv preprint arXiv:math/0411465},
year = {2014}
}
Comments
38 pages, 17 figures, minor modifications and corrections