Local Floer homology and infinitely many simple Reeb orbits

Abstract

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.

21 pages, many small mistakes and typos corrected

References in corpus (3)

• Functors and Computations in Floer homology with Applications Part II
• Floer homology of cotangent bundles and the loop product
• Computability and the growth rate of symplectic homology

Cited by in corpus (2)

• On the symplectic cohomology of log Calabi-Yau surfaces
• Morse theory, closed geodesics, and the homology of free loop spaces