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...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/536862 |
| Acceso en línea: | http://hdl.handle.net/2072/536862 |
| Access Level: | acceso abierto |
| Palabra clave: | b-symplectic manifolds Hamiltonian actions log-symplectic manifolds Marsden-Weinstein reduction Poisson structures Singular symplectic manifolds |
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Reduction theory for singular symplectic manifolds and singular forms on moduli spacesMatveeva, A.Miranda, E.b-symplectic manifoldsHamiltonian actionslog-symplectic manifoldsMarsden-Weinstein reductionPoisson structuresSingular symplectic manifoldsThe 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)The project that gave rise to these results received the support of a fellowship from “la Caixa” Foundation (ID 100010434) under the INPHINIT 2018 program for excellence centers. The grant is attached to the retained excellence project Interactions between symmetries and singularities in Geometry and Physics supervised by Eva Miranda. The fellowship code is LCF/BQ/DI18/11660046. Anastasia Matveeva and Eva Miranda are partially supported by the Spanish State Research Agency, through the grant PID2019-103849GB-I00 of AEI /10.13039/501100011033.Eva Miranda is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2016 and an ICREA Academia Prize 2021 and by a Friedrich Wilhelm Bessel Research Award of the Alexander von Humboldt Foundation. She is also partially supported by the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (project CEX2020-001084-M) and by the AGAUR-Gencat project number 2021 SGR 00603.Academic Press Inc.2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersion35 p.application/pdfhttp://hdl.handle.net/2072/536862RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésAdvances in MathematicsThis Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).https://rightsstatements.org/page/InC/1.0/?language=eninfo:eu-repo/semantics/openAccessoai:recercat.cat:2072/5368622026-05-29T05:05:01Z |
| dc.title.none.fl_str_mv |
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces |
| title |
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces |
| spellingShingle |
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces Matveeva, A. b-symplectic manifolds Hamiltonian actions log-symplectic manifolds Marsden-Weinstein reduction Poisson structures Singular symplectic manifolds |
| title_short |
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces |
| title_full |
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces |
| title_fullStr |
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces |
| title_full_unstemmed |
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces |
| title_sort |
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces |
| dc.creator.none.fl_str_mv |
Matveeva, A. Miranda, E. |
| author |
Matveeva, A. |
| author_facet |
Matveeva, A. Miranda, E. |
| author_role |
author |
| author2 |
Miranda, E. |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
b-symplectic manifolds Hamiltonian actions log-symplectic manifolds Marsden-Weinstein reduction Poisson structures Singular symplectic manifolds |
| topic |
b-symplectic manifolds Hamiltonian actions log-symplectic manifolds Marsden-Weinstein reduction Poisson structures Singular symplectic manifolds |
| description |
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) |
| publishDate |
2023 |
| dc.date.none.fl_str_mv |
2023 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion |
| format |
article |
| status_str |
submittedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/2072/536862 |
| url |
http://hdl.handle.net/2072/536862 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Advances in Mathematics |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
35 p. application/pdf |
| dc.publisher.none.fl_str_mv |
Academic Press Inc. |
| publisher.none.fl_str_mv |
Academic Press Inc. |
| dc.source.none.fl_str_mv |
RECERCAT (Dipòsit de la Recerca de Catalunya) reponame:Recercat. Dipósit de la Recerca de Catalunya instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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Recercat. Dipósit de la Recerca de Catalunya |
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Recercat. Dipósit de la Recerca de Catalunya |
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