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arXiv · 1404.6157

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 \cite{Eli89}. 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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Matthew Strom Borman, Yakov Eliashberg, Emmy Murphy. 2014-10-12. Existence and classification of overtwisted contact structures in all dimensions. https://arxiv.org/abs/1404.6157

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