Orderability and the Weinstein Conjecture

Abstract

In this article we prove that the Weinstein conjecture holds for contact manifolds $(\Sigma ,\xi )$ for which ${\mathrm{Cont}}_0(\Sigma ,\xi )$ 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.

arXiv comment22 pages; v3: major revision

References in corpus (8)

• Compactness results in Symplectic Field Theory
• Geometry of contact transformations and domains: orderability versus squeezing
• Leaf-wise intersections and Rabinowitz Floer homology
• A Morse estimate for translated points of contactomorphisms of spheres and projective spaces
• On iterated translated points for contactomorphisms of R^{2n+1} and R^{2n} x S^1
• Constructions controlees de champs de Reeb et applications
• Translated points and Rabinowitz Floer homology
• Target-local Gromov compactness

Cited by in corpus (4)

• Symplectic homology and the Eilenberg-Steenrod axioms
• Rigid constellations of closed Reeb orbits
• Positive loops and $L^{\infty }$-contact systolic inequalities
• Computing the Rabinowitz Floer homology of tentacular hyperboloids