Whitney stratifications are conically smooth

Abstract The notion of conically smooth structure on a stratified space was introduced by Ayala, Francis and Tanaka. This is very well behaved analogue differential in the context topological spaces, satisfying good properties such as existence resolutions singularities handlebody decompositions. In this paper we prove Tanaka’s conjecture that any Whitney admits canonical structure. We thus establish connection between theory spaces classical examples from topology.