Whitney stratification

Summary

A Whitney stratification of a singular space is a partition into smooth manifolds, the strata, see the definition. The strata fit together in a controlled way along their boundaries. The control is given by Whitney's conditions (a) and (b) on limits of tangent planes and secant lines. Hassler Whitney proved that every complex analytic set has such a stratification, and the result was later extended to semialgebraic and subanalytic sets. By the Thom–Mather isotopy theorem, a Whitney stratified space is topologically locally trivial along each stratum. This makes these stratifications the standard setting for perverse sheaves and intersection homology.