Gradient-like vector fields on a complex analytic variety

Details Gradient-like vector fields on a complex analytic variety Gradient-like vector fields on a complex analytic variety

2009-08-13

arxiv.org/abs/0908.1862v3

Mathematics

Geometric Topology

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

Scientific paper

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.

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