Gradient-like flows and self-indexing in stratified Morse theory

Details Gradient-like flows and self-indexing in stratified Morse theory Gradient-like flows and self-indexing in stratified Morse theory

2000-06-21

arxiv.org/abs/math/0006163v2

Mathematics

Algebraic Geometry

19 pages, AMS-LaTeX, replaced with revised version

Scientific paper

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.

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