Local Floer homology and infinitely many simple Reeb orbits

Details Local Floer homology and infinitely many simple Reeb orbits Local Floer homology and infinitely many simple Reeb orbits

2012-02-02

arxiv.org/abs/1202.0528v1

Mathematics

Symplectic Geometry

20 pages

Scientific paper

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 contangent 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.

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