Maximal symplectic torus actions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909940677869568 |
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| author | Henigman, Rei |
| author_facet | Henigman, Rei |
| contents | There are several different notions of maximal torus actions on smooth manifolds, in various contexts: symplectic, Riemannian, complex. In the symplectic context, for the so-called isotropy-maximal actions, as well as for the weaker notion of almost isotropy-maximal actions, we give classifications up to equivariant symplectomorphism. These classification results give symplectic analogues of recent classifications in the complex and Riemannian contexts. Moreover, we deduce that every almost isotropy-maximal symplectic torus action is equivariantly diffeomorphic to a product of a symplectic toric manifold and a torus, answering a question of Ishida. The classification theorems are consequences of Duistermaat and Pelayo's classification of symplectic torus actions with coisotropic orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal symplectic torus actions Henigman, Rei Symplectic Geometry Differential Geometry 53D20, 53D35, 37J15 There are several different notions of maximal torus actions on smooth manifolds, in various contexts: symplectic, Riemannian, complex. In the symplectic context, for the so-called isotropy-maximal actions, as well as for the weaker notion of almost isotropy-maximal actions, we give classifications up to equivariant symplectomorphism. These classification results give symplectic analogues of recent classifications in the complex and Riemannian contexts. Moreover, we deduce that every almost isotropy-maximal symplectic torus action is equivariantly diffeomorphic to a product of a symplectic toric manifold and a torus, answering a question of Ishida. The classification theorems are consequences of Duistermaat and Pelayo's classification of symplectic torus actions with coisotropic orbits. |
| title | Maximal symplectic torus actions |
| topic | Symplectic Geometry Differential Geometry 53D20, 53D35, 37J15 |
| url | https://arxiv.org/abs/2412.17126 |