Remarks on symplectic circle actions, torsion and loops
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909264603250688 |
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| author | Atallah, Marcelo S. |
| author_facet | Atallah, Marcelo S. |
| contents | We study loops of symplectic diffeomorphisms of closed symplectic manifolds. Our main result, which is valid for a large class of symplectic manifolds, shows that the flux of a symplectic loop vanishes whenever its orbits are contractible. As a consequence, we obtain a new vanishing result for the flux group and new instances where the presence of a fixed point of a symplectic circle action is a sufficient condition for it to be Hamiltonian. We also obtain applications to symplectic torsion, more precisely, non-trivial elements of $\mathrm{Symp}_{0}(M,ω)$ that have finite order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06392 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Remarks on symplectic circle actions, torsion and loops Atallah, Marcelo S. Symplectic Geometry Differential Geometry Dynamical Systems Geometric Topology 53D22, 53D40, 57R17, 57S15, 57S17 We study loops of symplectic diffeomorphisms of closed symplectic manifolds. Our main result, which is valid for a large class of symplectic manifolds, shows that the flux of a symplectic loop vanishes whenever its orbits are contractible. As a consequence, we obtain a new vanishing result for the flux group and new instances where the presence of a fixed point of a symplectic circle action is a sufficient condition for it to be Hamiltonian. We also obtain applications to symplectic torsion, more precisely, non-trivial elements of $\mathrm{Symp}_{0}(M,ω)$ that have finite order. |
| title | Remarks on symplectic circle actions, torsion and loops |
| topic | Symplectic Geometry Differential Geometry Dynamical Systems Geometric Topology 53D22, 53D40, 57R17, 57S15, 57S17 |
| url | https://arxiv.org/abs/2212.06392 |