Reduction theory for singular symplectic manifolds and singular forms on moduli spaces
The investigation of symmetries of b-symplectic manifolds and folded-symplectic manifolds is well-understood when the group under consideration is a torus (see, for instance, [GMPS, GLPR,GMW18a]forb-symplecticmanifoldsand [CGP,CM]forfoldedsymplecticmanifolds). However, reduction theory has not been...
| Autores: | , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/376370 |
| Acceso en línea: | https://hdl.handle.net/2117/376370 https://dx.doi.org/https://doi.org/10.48550/arXiv.2205.12919 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential geometry Differential Geometry Geometria diferencial Classificació AMS::53 Differential geometry Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial |
| Sumario: | The investigation of symmetries of b-symplectic manifolds and folded-symplectic manifolds is well-understood when the group under consideration is a torus (see, for instance, [GMPS, GLPR,GMW18a]forb-symplecticmanifoldsand [CGP,CM]forfoldedsymplecticmanifolds). However, reduction theory has not been set in this realm in full generality. This is fundamental, among other reasons, to advance in the “quantization commutes with reduction” programme for these manifolds initiated in [GMW18b, GMW21]. In this article, we fill in this gap and investigate the MarsdenWeinstein reductiontheory under generalsymmetriesforgeneralbm-symplecticmanifoldsand other singular symplectic manifolds, including certain folded symplectic manifolds. In this new framework, the set of admissible Hamiltonian functions is larger than the category of smooth functions as it takes the singularities of the differential forms into account. The quasi-Hamiltonian set-up is also considered and brand-new constructions of (singular) quasi-Hamiltonian spaces are obtained via a reduction procedure and the fusion product. |
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