Stratified Morse Theory with Tangential Conditions
Abstract
Our objective is to develop a stratified Morse theory with tangential conditions. We define a continuous strata-wise smooth Morse function on an abstract stratified space by using control conditions and radiality assumptions on the gradient vector field. For critical points of a Morse function one can show that the local unstable set is a manifold and the local stable set is itself an abstract stratified space. We also give a normal form for the gradient dynamics in the neighborhood of critical points. For a stratified Morse pair which satisfies the generic Morse-Smale condition we can build the Morse-Witten complex and show that its homology is equivalent to the singular homology of the space.
Cite
@article{arxiv.math/0310019,
title = {Stratified Morse Theory with Tangential Conditions},
author = {Ursula Ludwig},
journal= {arXiv preprint arXiv:math/0310019},
year = {2010}
}
Comments
This paper has been withdrawn by the author. Part of this article has been published in revised form under the title "Morse-Smale-Witten complex for gradient-like vector fields on stratified spaces" in Ch\'eniot, Denis (ed.) et al., Singularity theory. Proceedings of the 2005 Marseille singularity school and conference