Gradient-like Vector Fields on a Complex Analytic Variety Cheol-hyun Cho and Giovanni Marelli

Abstract

Given any Morse function f on a Whitney stratified complex analytic variety of complex dimension n, we prove the existence of a stratified gradient-like vector field for 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. 

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