Vanishing of Rabinowitz Floer homology on negative line bundles
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2015
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| _version_ | 1866918232338726912 |
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| author | Albers, Peter Kang, Jungsoo |
| author_facet | Albers, Peter Kang, Jungsoo |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1508_02525 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Vanishing of Rabinowitz Floer homology on negative line bundles Albers, Peter Kang, Jungsoo Symplectic Geometry 53D40 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]. |
| title | Vanishing of Rabinowitz Floer homology on negative line bundles |
| topic | Symplectic Geometry 53D40 |
| url | https://arxiv.org/abs/1508.02525 |