A note on the symplectic classification of almost-toric systems
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913540418306048 |
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| author | Tang, Xiudi |
| author_facet | Tang, Xiudi |
| contents | Since simple semitoric systems were classified about fifteen years ago, and semitoric systems five years ago, we want to move a step forward to almost-toric systems. We give a classification of compact almost-toric systems in dimension four up to fiber-preserving symplectomorphisms, in terms of the base, Taylor series, and twisting indices, analogous to the five invariants for semitoric systems. For convenience, we specify an ordering of focus-focus values and a choice of two cut rays at each of them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08175 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the symplectic classification of almost-toric systems Tang, Xiudi Symplectic Geometry Differential Geometry Dynamical Systems 53D20 (Primary) 53A15 (Secondary) Since simple semitoric systems were classified about fifteen years ago, and semitoric systems five years ago, we want to move a step forward to almost-toric systems. We give a classification of compact almost-toric systems in dimension four up to fiber-preserving symplectomorphisms, in terms of the base, Taylor series, and twisting indices, analogous to the five invariants for semitoric systems. For convenience, we specify an ordering of focus-focus values and a choice of two cut rays at each of them. |
| title | A note on the symplectic classification of almost-toric systems |
| topic | Symplectic Geometry Differential Geometry Dynamical Systems 53D20 (Primary) 53A15 (Secondary) |
| url | https://arxiv.org/abs/2410.08175 |