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arXiv · 1512.06208

Periodic Reeb flows and products in symplectic homology

Peter Uebele
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Abstract

In this paper, we explore the structure of Rabinowitz--Floer homology $RFH_*$ on contact manifolds whose Reeb flow is periodic (and which satisfy an index condition such that $RFH_*$ is independent of the filling). The main result is that $RFH_*$ 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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Peter Uebele. 2015-12-19. Periodic Reeb flows and products in symplectic homology. https://arxiv.org/abs/1512.06208

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