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Vanishing of Rabinowitz Floer homology on negative line bundles

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Following Frauenfelder (Rabinowitz action functional on very negative line bundles, Habilitationsschrift, Munich/München, 2008), Albers and Frauenfelder (Bubbles and onis, 2014. arXiv:1412.4360) we construct Rabinowitz Floer homology for negative line bundles over symplectic manifolds and prove a vanishing result. Ritter (Adv Math 262:1035–1106, 2014) showed that symplectic homology of these spaces does not vanish, in general. Thus, the theorem \(\mathrm {SH}=0\Leftrightarrow \mathrm {RFH}=0\) (Ritter in J Topol 6(2):391–489, 2013), does not extend beyond the symplectically aspherical situation. We give a conjectural explanation in terms of the Cieliebak–Frauenfelder–Oancea long exact sequence Cieliebak et al. (Ann Sci Éc Norm Supér (4) 43(6):957–1015, 2010).

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Acknowledgments

We thank Urs Frauenfelder for illuminating discussion on the present article. PA is supported by SFB 878. JK is supported by DFG Grant KA 4010/1-1.

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  1. Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Münster, Germany

    Peter Albers & Jungsoo Kang

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  1. Peter Albers
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  2. Jungsoo Kang
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Correspondence to Peter Albers.

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Albers, P., Kang, J. Vanishing of Rabinowitz Floer homology on negative line bundles. Math. Z. 285, 493–517 (2017). https://doi.org/10.1007/s00209-016-1718-6

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