On the smooth Whitney fibering conjecture

C. Murolo*, A. du Plessis*, D. J.A. Trotman*

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Abstract

We improve upon the first Thom–Mather isotopy theorem for Whitney stratified sets. In particular, for the more general Bekka stratified sets we show that there is a local foliated structure with continuously varying tangent spaces, thus proving the smooth version of the Whitney fibering conjecture. A regular wing structure is also shown to exist locally, for Bekka stratifications. The proofs involve integrating carefully chosen controlled distributions of vector fields. As an application of our main theorem, we show the density of the subset of strongly topologically stable mappings in the space of all smooth quasi-proper mappings between smooth manifolds, an improvement of a theorem of Mather.

Original languageEnglish
Article numbere70021
JournalJournal of the London Mathematical Society
Volume110
Issue6
ISSN0024-6107
DOIs
Publication statusPublished - Dec 2024

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