Orderability and the Weinstein Conjecture

Abstract

In this article we prove that the Weinstein conjecture holds for contact manifolds $(Σ,ξ)$ for which $\mathrm{Cont}_0(Σ,ξ)$ is non-orderable in the sense of Eliashberg-Polterovich [EP00]. More precisely, we establish a link between orderable and hypertight contact manifolds. In addition, we prove for certain contact manifolds a conjecture by Sandon [San13b] on the existence of translated points in the non-degenerate case.

22 pages; v3: major revision