Periodic Reeb flows and products in symplectic homology

In this paper, we explore the structure of Rabinowitz–Floer homology $\mathop{RFH}_{\ast}$ on contact manifolds whose Reeb flow is periodic (and which satisfy an index condition such that $\mathop{RFH}_{\ast}$ is independent of the filling). The main result is that $\mathop{RFH}_{\ast}$ 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.

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Received 13 July 2016

Accepted 18 August 2018

Published 24 October 2019