Existence and classification of overtwisted contact structures in all dimensions

Matthew Strom Borman, Yakov Eliashberg, Emmy Murphy

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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 languageEnglish (US)
Pages (from-to)281-361
Number of pages81
JournalActa Mathematica
Volume215
Issue number2
DOIs
Publication statusPublished - Dec 1 2015
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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