Morse-Conley-Floer homology

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.