复解析簇上的类似向量场
Gradient-like vector fields on a complex analytic variety
摘要：
给定复维数n的Whitney分层复解析簇上的复解析函数f，其实部Re（f）为Morse，我们证明了Re（f）的分层类梯度向量场的存在性，使得复维数s的层S上临界点p的不稳定集具有Goresky和MacPherson所证明的实维数$m(p)+n-s$.
英文摘要：
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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