Maximal symplectic torus actions

Fuente: arXiv
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Autore principale: Henigman, Rei
Natura: Preprint
Pubblicazione: 2024
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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