Gradient-like flows and self-indexing in stratified Morse theory
Algebraic Geometry
2007-05-23 v2 Dynamical Systems
Abstract
We develop the idea of self-indexing and the technology of gradient-like vector fields in the setting of Morse theory on a complex algebraic stratification. Our main result is the local existence, near a Morse critical point, of gradient-like vector fields satisfying certain ``stratified dimension bounds up to fuzz'' for the ascending and descending sets. As a global consequence of this, we derive the existence of self-indexing Morse functions.
Keywords
Cite
@article{arxiv.math/0006163,
title = {Gradient-like flows and self-indexing in stratified Morse theory},
author = {Mikhail Grinberg},
journal= {arXiv preprint arXiv:math/0006163},
year = {2007}
}
Comments
19 pages, AMS-LaTeX, replaced with revised version