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September 2017 Regularization and minimization of codimension-one Haefliger structures
Gaël Meigniez
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J. Differential Geom. 107(1): 157-202 (September 2017). DOI: 10.4310/jdg/1505268031

Abstract

On compact manifolds of dimensions $4$ and more, we give a proof of Thurston’s existence theorem for foliations of codimension one; that is, they satisfy some $h$-principle in the sense of Gromov. Our proof is an explicit construction not using the Mather homology equivalence. Moreover, the produced foliations are minimal, that is, all leaves are dense. In particular, there exist minimal, $C^{\infty}$, codimension-one foliations on every closed connected manifold of dimension at least $4$ whose Euler characteristic is zero.

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Gaël Meigniez. "Regularization and minimization of codimension-one Haefliger structures." J. Differential Geom. 107 (1) 157 - 202, September 2017. https://doi.org/10.4310/jdg/1505268031

Information

Received: 7 May 2012; Published: September 2017
First available in Project Euclid: 13 September 2017

zbMATH: 06846963
MathSciNet: MR3698236
Digital Object Identifier: 10.4310/jdg/1505268031

Subjects:
Primary: 57R30

Rights: Copyright © 2017 Lehigh University

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Vol.107 • No. 1 • September 2017
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