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Orderability and the Weinstein conjecture
- Part of
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- Journal:
- Compositio Mathematica / Volume 151 / Issue 12 / December 2015
- Published online by Cambridge University Press:
- 24 September 2015, pp. 2251-2272
- Print publication:
- December 2015
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- Article
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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.
