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.

arXiv comment86 pages, 16 figures

References in corpus (7)

• Geometry of contact transformations and domains: orderability versus squeezing
• Brieskorn manifolds in contact topology
• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• Contact structures on 5-manifolds
• Geometric criteria for overtwistedness
• On the non-existence of small positive loops of contactomorphisms on overtwisted contact manifolds
• H-principle for 4-dimensional contact foliations

Cited by in corpus (1)

• The fundamental group and Betti numbers of toric origami manifolds