Local contact homology and applications

Abstract

We introduce a local version of contact homology for an isolated periodic orbit of the Reeb flow and prove that its rank is uniformly bounded for isolated iterations. Several applications are obtained, including a generalization of Gromoll-Meyer's theorem on the existence of infinitely many simple periodic orbits, resonance relations and conditions for the existence of non-hyperbolic periodic orbits.

62 pages. We would like to thank Michael Hutchings for pointing out a problem in our previous attempt to define local contact homology using domain-dependent almost complex structures. For more details see http://floerhomology.wordpress.com/2013/09/08/an-obstruction-to-cylindrical-contact-homology/