Existence and classification of overtwisted contact structures in all dimensions

Matthew Strom Borman; Yakov Eliashberg; Emmy Murphy

doi:10.1007/s11511-016-0134-4

Existence and classification of overtwisted contact structures in all dimensions

Matthew Strom Borman, Yakov Eliashberg, Emmy Murphy

Mathematics

Research output: Contribution to journal › Article › peer-review

77 Scopus citations

Abstract

We establish a parametric extension h-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the 3-dimensional result from [12]. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of almost contact structures.

Original language	English (US)
Pages (from-to)	281-361
Number of pages	81
Journal	Acta Mathematica
Volume	215
Issue number	2
DOIs	https://doi.org/10.1007/s11511-016-0134-4
State	Published - Dec 1 2015

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11511-016-0134-4

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title = "Existence and classification of overtwisted contact structures in all dimensions",

abstract = "We establish a parametric extension h-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the 3-dimensional result from [12]. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of almost contact structures.",

author = "Borman, {Matthew Strom} and Yakov Eliashberg and Emmy Murphy",

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AU - Eliashberg, Yakov

AU - Murphy, Emmy

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AB - We establish a parametric extension h-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the 3-dimensional result from [12]. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of almost contact structures.

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Existence and classification of overtwisted contact structures in all dimensions

Abstract

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