Peter Uebele | Searcharxiv

arXiv2019

Periodic Reeb flows and products in symplectic homology

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.

math.SG↗

arXiv2016

Symplectic homology of some Brieskorn manifolds

This paper consists of two parts. In the first part, we use symplectic homology to distinguish the contact structures on the Brieskorn manifolds $Σ(2l,2,2,2)$, which contact homology cannot distinguish. This answers a question from [22]. In the second part, we prove the existence of infinitely many exotic but homotopically trivial exotic contact structures on $S^7$, distinguished by the mean Euler characteristic of $S^1$-equivariant symplectic homology. Apart from various connected sum constructions, these contact structures can be taken from the Brieskorn manifolds $Σ(78k+1,13,6,3,3)$. We end with some considerations about extending this result to higher dimensions.

math.SG↗