Morse Cells

TL;DR

This paper demonstrates that for a generic gradient-like vector field on a manifold with a Morse function, the stable manifolds form a CW decomposition, extending known results to a broader context.

Contribution

It generalizes the known CW decomposition result to manifolds with corners and stratifications, providing new insights into the topology of such manifolds.

Findings

Stable manifolds form a CW decomposition in the given setting

Extension of Morse theory results to manifolds with corners

Application of stratification techniques to Morse functions

Abstract

Along with excursions into manifolds with corners, resolution towers of Thom and Whitney stratifications, I show that for a generic gradientlike vector field on a manifold with a Morse function, the stable manifolds give a CW decomposition of the manifold. This has been done before.