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 \cite{Eli89}. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of almost contact structures.

86 pages, 16 figures

References in corpus (3)

• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• Contact structures on 5-manifolds
• On the non-existence of small positive loops of contactomorphisms on overtwisted contact manifolds