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, [25,21,28] for b-symplectic manifolds and [12,14] for folded symplectic manifolds). However, reduction theory has not been se...
| Authors: | ; |
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| Format: | Article |
| Status: | Submitted version |
| Publication date: | 2023 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/536862 |
| Online Access: | http://hdl.handle.net/2072/536862 |
| Access Level: | Open access |
| Keyword: | b-symplectic manifolds Hamiltonian actions log-symplectic manifolds Marsden-Weinstein reduction Poisson structures Singular symplectic manifolds |
| Summary: | 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, [25,21,28] for b-symplectic manifolds and [12,14] for folded symplectic manifolds). 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 [29,30]. In this article, we fill in this gap and investigate the Marsden-Weinstein reduction theory under general symmetries for general bm-symplectic manifolds and 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. © 2023 The Author(s) |
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