Towards a classification of toric and semitoric singular symplectic manifolds
In this article, we present a classification of toric -symplectic manifolds and outline a program for the classification of semitoric singular symplectic manifolds. As a testing ground, we begin with the case of -symplectic manifolds, where a Delzant-type theorem for toric actions has already been e...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:dnet:upcommonspor::eb2bc1c62a6957bf28ebaece1047831e |
| Acceso en línea: | https://hdl.handle.net/2117/460497 https://dx.doi.org/10.1134/S1560354726020036 |
| Access Level: | acceso abierto |
| Palabra clave: | Integrable systems Toric manifolds Semitoric manifolds B-symplectic manifolds Logsymplectic manifolds Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
| Sumario: | In this article, we present a classification of toric -symplectic manifolds and outline a program for the classification of semitoric singular symplectic manifolds. As a testing ground, we begin with the case of -symplectic manifolds, where a Delzant-type theorem for toric actions has already been established [13]. Building on this foundation, we extend the framework to the broader setting of -symplectic manifolds, thereby establishing the first classification result for -toric manifolds. This achievement lays the groundwork for a conjectural classification theory of semitoric systems in dimension four on -symplectic manifolds. Furthermore, by employing the reduction theory developed in [21], we propose a conjectural classification scheme for higher-dimensional semitoric manifolds, aiming to generalize the Pelayo – Vu Ng¿c classification program [32, 33] to the singular -setting. |
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