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arXiv · 1305.4074

Morse-Conley-Floer Homology

T. O. Rot·R. C. A. M. Vandervorst
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Abstract

For Morse-Smale pairs on a smooth, closed manifold the Morse-Smale-Witten chain complex can be defined. The associated Morse homology is isomorphic to the singular homology of the manifold and yields the classical Morse relations for Morse functions. A similar approach can be used to define homological invariants for isolated invariant sets of flows on a smooth manifold, which gives an analogue of the Conley index and the Morse-Conley relations. The approach will be referred to as Morse-Conley-Floer homology.

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T. O. Rot, R. C. A. M. Vandervorst. 2014-04-23. Morse-Conley-Floer Homology. https://doi.org/10.1142/s1793525314500174

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