Year: 2015
Type: article
Abstract: In this article we prove that the Weinstein conjecture holds for contact manifolds $({\rm\Sigma},{\it\xi})$ for which $\text{Cont}_{0}({\rm\Sigma},{\it\xi})$ is non-orderable in the sense of Eliashberg and Polterovich [ Partially ordered groups and geometry of contact transformations , Geom. Funct. Anal. 10 (2000), 1448–1476]. More precisely, we establish a link between orderable and hypertight contact manifolds. In addition, we prove for certain contact manifolds a conjecture by Sandon [ A Morse estimate for translated points of contactomorphisms of spheres and projective spaces , Geom. Dedicata 165 (2013), 95–110] on the existence of translated points in the non-degenerate case.
Source: Compositio Mathematica
Authors: Peter Albers, Urs Fuchs, Will J. Merry
Institutions: University of Münster, Ruhr University Bochum, ETH Zurich
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1550345142