Whitney's fibering conjecture

Let $V$ be an analytic subvariety of an open set $U\subset\mathbb{C}^n$. A stratification of $V$ is a decomposition into strata as in Whitney's regularity conditions. A semi-analytic fibration on a neighborhood $U_0$ of a point $p_0\in V$ is a local fibration of the stratified set into submanifolds isomorphic to the strata.

Whitney's fibering conjecture. Every analytic subvariety $V\subset U$ has a stratification such that each point $p_0\in V$ has a neighborhood $U_0$ with a semi-analytic fibration.

Whitney's conjecture asks for a local fibering stronger than the topological triviality supplied by the regularity conditions (a) and (b). It was proven in the local complex and real analytic cases, and in global algebraic cases, by means of Zariski equisingularity and arc-wise analytic triviality.