A correspondence between a class of cone structures and contact forms

Mélanie Bertelson; Cédric De Groote

paper

A correspondence between a class of cone structures and contact forms

arXiv:1504.08149

Abstract

In the spirit of Sullivan's paper "Cycles for the Dynamical Study of Foliated Manifolds and Complex Manifolds", existence of a contact structure on a closed manifold $M$ is shown to be equivalent to existence of an ample $S^{1}$ -invariant cone structure with no nontrivial exact structure cycles on the manifold $S^{1} \times M$ .

14 pages