Abstract
The gradient flow of a Morse function on a smooth closed manifold generates, under suitable transversality assumptions, the Morse-Smale-Witten complex. The associated Morse homology is an invariant for the manifold, and equals the singular homology, which yields the classical Morse relations. In this paper we define Morse-Conley-Floer homology, which is an analogous homology theory for isolated invariant sets of smooth, not necessarily gradient-like, flows. We prove invariance properties of the Morse-Conley-Floer homology, and show how it gives rise to the Morse-Conley relations. © 2014 World Scientific Publishing Company.
Original language | English |
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Pages (from-to) | 305-338 |
Journal | Journal of Topology and Analysis |
Volume | 6 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2014 |