Periodic symplectic and Hamiltonian diffeomorphisms on irrational ruled surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915535360360448 |
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| author | Lindsay, Nicholas Zhang, Weiyi |
| author_facet | Lindsay, Nicholas Zhang, Weiyi |
| contents | We study the extension of homologically trivial symplectic or Hamiltonian cyclic actions to Hamiltonian circle actions on irrational ruled symplectic $4$-manifolds. On one hand, we construct symplectic involutions on minimal irrational ruled $4$-manifolds that cannot extend to a symplectic circle action even with a possibly different symplectic form. Higher dimensional examples are also constructed. On the other hand, for homologically trivial symplectic cyclic actions of any other order, we show that such an extension always exists.
We also classify finite groups of symplecticmorphisms that acts trivially on the first homology group, and prove the non-extendability of the Klein $4$-group action to the three dimensional rotation group action motivated by the classification of finite groups of symplectomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18580 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periodic symplectic and Hamiltonian diffeomorphisms on irrational ruled surfaces Lindsay, Nicholas Zhang, Weiyi Symplectic Geometry Geometric Topology We study the extension of homologically trivial symplectic or Hamiltonian cyclic actions to Hamiltonian circle actions on irrational ruled symplectic $4$-manifolds. On one hand, we construct symplectic involutions on minimal irrational ruled $4$-manifolds that cannot extend to a symplectic circle action even with a possibly different symplectic form. Higher dimensional examples are also constructed. On the other hand, for homologically trivial symplectic cyclic actions of any other order, we show that such an extension always exists. We also classify finite groups of symplecticmorphisms that acts trivially on the first homology group, and prove the non-extendability of the Klein $4$-group action to the three dimensional rotation group action motivated by the classification of finite groups of symplectomorphisms. |
| title | Periodic symplectic and Hamiltonian diffeomorphisms on irrational ruled surfaces |
| topic | Symplectic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2411.18580 |