Quasicomplementary foliations and the Mather–Thurston theorem

Meigniez, Gaël

doi:10.2140/gt.2021.25.643

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Quasicomplementary foliations and the Mather–Thurston theorem

Gaël Meigniez

Geometry & Topology 25 (2021) 643–710

DOI: 10.2140/gt.2021.25.643

Abstract

We establish a form of the h–principle for the existence of foliations of codimension at least $2$ which are quasicomplementary to a given one. Roughly, “quasicomplementary” means that they are complementary except on the boundaries of some kind of Reeb components. The construction involves an adaptation of W Thurston’s “inflation” process. The same methods also provide a proof of the classical Mather–Thurston theorem.

Keywords

foliation, Haefliger structure, h–principle, Mather–Thurston theorem, Thurston's inflation

Mathematical Subject Classification 2010

Primary: 57R30, 57R32, 58H10

References

Publication

Received: 22 August 2018

Revised: 10 April 2020

Accepted: 20 May 2020

Published: 27 April 2021

Proposed: Yasha Eliashberg

Seconded: David Gabai, Mladen Bestvina

Authors

Gaël Meigniez
Laboratoire de Mathématiques de Bretagne Atlantique Université de Bretagne Sud (LMBA UBS, UMR CNRS 6205) Vannes France

Volume 25, issue 2 (2021)