2009/08/13 by Cheol‐Hyun Cho, Cho, Cheol-Hyun, G. Marelli +1 · 1 citation
Mathematics · #32C42 #37D15 #55N33 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT)
paper · pdf · doi:10.48550/arxiv.0908.1862
openalex publication_date 2009/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.