Existence and classification of overtwisted contact structures in all dimensions

2014/04/24 by Borman, Matthew Strom, Eliashberg, Yakov, Murphy, Emmy · 5 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1404.6157

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 \citeEli89. 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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