Local Floer homology and infinitely many simple Reeb orbits

McLean, Mark¹

¹Department of Mathematics, MIT, Building 2, Room 275, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA

Algebraic and Geometric Topology, Tome 12 (2012) no. 4, pp. 1901-1923

Résumé

Let Q be a Riemannian manifold such that the Betti numbers of its free loop space with respect to some coefficient field are unbounded. We show that every contact form on its unit cotangent bundle supporting the natural contact structure has infinitely many simple Reeb orbits. This is an extension of a theorem by Gromoll and Meyer. We also show that if a compact manifold admits a Stein fillable contact structure then there is a possibly different such structure which also has infinitely many simple Reeb orbits for every supporting contact form. We use local Floer homology along with symplectic homology to prove these facts.

Détail

DOI : 10.2140/agt.2012.12.1901

Classification : 53D10, 53D25, 53D40
Keywords: symplectic homology, local Floer, cotangent bundle, Reeb orbits

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