Volume 25, issue 2 (2021)

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Quasicomplementary foliations and the Mather–Thurston theorem

Gaël Meigniez

Geometry & Topology 25 (2021) 643–710
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