Séance Séminaire

Séminaire Gaston Darboux

Geometrie locale des espaces singuliers et conjecture de Whitney

Since the foundational work of Whitney and Thom much progress has been made in taming real and complex algebraic/analytic varieties. Whitney showed the existence of (b)-regular stratifications which Thom proved to be locally topologically trivial. Hardt showed further local semialgebraic triviality of semialgebraic sets, while Mostowski and Parusinski showed local bilipschitz triviality. Recently Valette combined these results by obtaining local semialgebraic bilipschitz triviality of semialgebraic sets, and proved a conjecture of Siebenmann and Sullivan on the countability of metric types of germs of analytic spaces. Whitney's fibering conjecture asks that a neighbourhood of a stratum be foliated by analytic copies of a core stratum such that the tangent spaces to the leaves of the foliation vary continuously. We describe recent progress made with Murolo and du Plessis on a subanalytic Whitney fibering conjecture and its smooth version. There are applications to other conjectures - for example Whitney triangulation of Whitney stratified sets (proved by Shiota in 2005 for semialgebraic sets).