Local contact homology and applications

Details Local contact homology and applications Local contact homology and applications

2012-02-14

arxiv.org/abs/1202.3122v1

Mathematics

Symplectic Geometry

46 pages

Scientific paper

We introduce a local version of contact homology for an isolated periodic orbit $\gamma$ 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.

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