Classification of symplectic non-Hamiltonian circle actions on 4-manifolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929592564973568 |
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| author | Henigman, Rei |
| author_facet | Henigman, Rei |
| contents | We classify symplectic non-Hamiltonian circle actions on compact connected symplectic 4-manifolds, up to equivariant symplectomorphisms. Namely, we define a set of invariants, show that the set is complete, and determine which values are attainable by constructing a space for each valid choice. We work under the assumption that the group of periods of the one-form $ι_X ω$ is discrete, which allows us to define a circle-valued Hamiltonian for the action, and apply tools from Karshon-Tolman's work on the classification of complexity one spaces. This assumption is always satisfied if the symplectic form is rational, or if the quotient space has first Betti number one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of symplectic non-Hamiltonian circle actions on 4-manifolds Henigman, Rei Symplectic Geometry 53D20, 53D35 We classify symplectic non-Hamiltonian circle actions on compact connected symplectic 4-manifolds, up to equivariant symplectomorphisms. Namely, we define a set of invariants, show that the set is complete, and determine which values are attainable by constructing a space for each valid choice. We work under the assumption that the group of periods of the one-form $ι_X ω$ is discrete, which allows us to define a circle-valued Hamiltonian for the action, and apply tools from Karshon-Tolman's work on the classification of complexity one spaces. This assumption is always satisfied if the symplectic form is rational, or if the quotient space has first Betti number one. |
| title | Classification of symplectic non-Hamiltonian circle actions on 4-manifolds |
| topic | Symplectic Geometry 53D20, 53D35 |
| url | https://arxiv.org/abs/2411.10157 |