Vanishing of Rabinowitz Floer homology on negative line bundles - Albers, Peter; Kang, Jungsoo (Mathematische Zeitschrift, 2017)
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 SH=0⇔RFH=0SH=0\Leftrightarrow 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).
Published online: 20 June 2016
Gesehen am 14.08.2017