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Orderability and the Weinstein conjecture

Albers, Peter ; Fuchs, Urs ; Merry, Will J.

In: Compositio Mathematica, 2015, vol. 151, no. 12, p. 2251-2272

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    Titre
    • Orderability and the Weinstein conjecture
    Auteur
    • Albers, Peter. Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Germany email peter.albers@wwu.de
    • Fuchs, Urs. Fakultät für Mathematik, Ruhr-Universität Bochum, Germany email urs.fuchs@rub.de
    • Merry, Will J.. Department of Mathematics, ETH Zürich, Switzerland email merry@math.ethz.ch
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Compositio Mathematica, 2015, vol. 151, no. 12, p. 2251-2272. London Mathematical Society
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:295623
    Summary
    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