Gradient-like vector fields on a complex analytic variety

Abstract

Given a complex analytic function f on a Whitney stratified complex analytic variety of complex dimension n, whose real part Re(f) is Morse, we prove the existence of a stratified gradient-like vector field for Re(f) such that the unstable set of a critical point p on a stratum S of complex dimension s has real dimension $m(p)+n-s$ as was conjectured by Goresky and MacPherson.

23 pages, 4 figure, v2:major revision, v3:added restriction on Morse function and removed fast condition

References in corpus (2)

• The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils
• Dimensions of the Ascending and Descending Sets in Complex Stratified Morse Theory

Cited by in corpus (1)

• Dimensions of the Ascending and Descending Sets in Complex Stratified Morse Theory