Vanishing of Rabinowitz Floer homology on negative line bundles
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 v...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2017
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| In: |
Mathematische Zeitschrift
Year: 2016, Volume: 285, Issue: 1/2, Pages: 493-517 |
| ISSN: | 1432-1823 |
| DOI: | 10.1007/s00209-016-1718-6 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s00209-016-1718-6 Verlag, Volltext: https://link.springer.com/article/10.1007/s00209-016-1718-6 
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| Author Notes: | Peter Albers, Jungsoo Kang |
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| 520 | |a 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=0\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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