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2021 Quasicomplementary foliations and the Mather–Thurston theorem
Gaël Meigniez
Geom. Topol. 25(2): 643-710 (2021). 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.

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Gaël Meigniez. "Quasicomplementary foliations and the Mather–Thurston theorem." Geom. Topol. 25 (2) 643 - 710, 2021. https://doi.org/10.2140/gt.2021.25.643

Information

Received: 22 August 2018; Revised: 10 April 2020; Accepted: 20 May 2020; Published: 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.2140/gt.2021.25.643

Subjects:
Primary: 57R30 , 57R32 , 58H10

Keywords: Foliation , Haefliger structure , h–principle , Mather–Thurston theorem , Thurston's inflation

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.25 • No. 2 • 2021
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