Morse-Conley-Floer Homology
Dynamical Systems
2014-09-11 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1305.4074,
title = {Morse-Conley-Floer Homology},
author = {T. O. Rot and R. C. A. M. Vandervorst},
journal= {arXiv preprint arXiv:1305.4074},
year = {2014}
}