English

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

R2 v1 2026-07-22T16:33:19.670Z