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arXiv · 1508.02525

Vanishing of Rabinowitz Floer homology on negative line bundles

Peter Albers·Jungsoo Kang
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Abstract

Following [Fra08, AF14] we construct Rabinowitz Floer homology for negative line bundles over symplectic manifolds and prove a vanishing result. In [Rit14] Ritter showed that symplectic homology of these spaces does not vanish, in general. Thus, the theorem $\mathrm{SH}=0\Leftrightarrow\mathrm{RFH}=0$, [Rit13], does not extend beyond the symplectically aspherical situation. We give a conjectural explanation in terms of the Cieliebak-Frauenfelder-Oancea long exact sequence [CFO10].

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Peter Albers, Jungsoo Kang. 2015-08-11. Vanishing of Rabinowitz Floer homology on negative line bundles. https://doi.org/10.1007/s00209-016-1718-6

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