Lectures on Twisted Rabinowitz-Floer Homology
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866912862206689280 |
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| author | Bähni, Yannis |
| author_facet | Bähni, Yannis |
| contents | Rabinowitz-Floer homology is the Morse-Bott homology in the sense of Floer associated with the Rabinowitz action functional introduced by Kai Cieliebak and Urs Frauenfelder in 2009. In this manuscript, we consider a generalisation of this theory to a Rabinowitz-Floer homology of a Liouville automorphism. As an application, we show the existence of noncontractible periodic Reeb orbits on quotients of symmetric star-shaped hypersurfaces. In particular, this theory applies to lens spaces. Moreover, we prove a forcing theorem, which guarantees the existence of a contractible twisted closed characteristic on a displaceable twisted stable hypersurface in a symplectically aspherical geometrically bounded symplectic manifold if there exists a contractible twisted closed characteristic belonging to a Morse-Bott component, with energy difference smaller or equal to the displacement energy of the displaceable hypersurface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_06649 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Lectures on Twisted Rabinowitz-Floer Homology Bähni, Yannis Symplectic Geometry 53D40, 37J10 Rabinowitz-Floer homology is the Morse-Bott homology in the sense of Floer associated with the Rabinowitz action functional introduced by Kai Cieliebak and Urs Frauenfelder in 2009. In this manuscript, we consider a generalisation of this theory to a Rabinowitz-Floer homology of a Liouville automorphism. As an application, we show the existence of noncontractible periodic Reeb orbits on quotients of symmetric star-shaped hypersurfaces. In particular, this theory applies to lens spaces. Moreover, we prove a forcing theorem, which guarantees the existence of a contractible twisted closed characteristic on a displaceable twisted stable hypersurface in a symplectically aspherical geometrically bounded symplectic manifold if there exists a contractible twisted closed characteristic belonging to a Morse-Bott component, with energy difference smaller or equal to the displacement energy of the displaceable hypersurface. |
| title | Lectures on Twisted Rabinowitz-Floer Homology |
| topic | Symplectic Geometry 53D40, 37J10 |
| url | https://arxiv.org/abs/2109.06649 |