Periodic Reeb flows and products in symplectic homology

Abstract

In this paper, we explore the structure of Rabinowitz--Floer homology $RF{H}_{\ast }$ on contact manifolds whose Reeb flow is periodic (and which satisfy an index condition such that $RF{H}_{\ast }$ is independent of the filling). The main result is that $RF{H}_{\ast }$ is a module over the Laurent polynomials ${\mathbb{Z}}_2[s,s^{-1}]$, where $s$ is the homology class generated by a principal Reeb orbit and the module structure is given by the pair-of-pants product. In most cases, this module is free and finitely generated.

33 pages, 5 figures. Several corrections. To appear in Journal of Symplectic Geometry