Morse-Smale Homology for compact manifolds and Invariant Sets

Abstract

The thesis consists in two parts. In the first part, we construct Morse-Smale homology groups on smooth, compact, finite-dimensional Riemannian manifolds and show that these homology groups are independent of the given Morse-Smale function. In the second part, we consider any manifold and define the Morse-Smale homology groups in insolated invariant sets which will also be independent of the chosen Morse-Smale function.