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The smooth Whitney fibering conjecture and Whitney cellulation

Banff International Research Station for Mathematical Innovation and Discovery

In a joint work with Claudio Murolo and Andrew du Plessis we proved the smooth Whitney fibering conjecture, in particular for every stratum X of a Whitney stratified set, locally near points of X the foliation defined by the Thom-Mather topological trivialization can be chosen, via suitable vector fields, so that the tangent spaces to the leaves are continuous at X. Moreover the associated wings have a similar property and are Whitney regular. As an application we describe a joint result with Claudio Murolo: every compact Whitney stratified set admits a Whitney cellulation, i.e. a cellulation such that the cells form a Whitney stratification. This resolves a homology problem of Mark Goresky.

Mathematics; Algebraic geometry; Several complex variables and analytic spaces

video/mp4

Author affiliation: Aix Marseille University

2019-04-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69893

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/