E-Structures and almost regular poisson manifolds

In recent years, b-symplectic manifolds have emerged as important objects in symplectic geometry. These manifolds are Poisson manifolds that exhibit symplectic behaviour away from a distinguished hypersurface, where the symplectic form degenerates in a controlled manner. Inspired by this rich landsc...

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Autores: Garmendia, Alfonso, Miranda Galcerán, Eva|||0000-0001-9518-5279
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::59162ad4df80dca3e3e8fbf78a5ddcc1
Acceso en línea:https://hdl.handle.net/2117/460490
https://dx.doi.org/10.1017/S1474748026101595
Access Level:acceso abierto
Palabra clave:Singular foliations
Symplectic structures
Lie algebroids
Poisson groupoids
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::57 Manifolds and cell complexes::57R Differential topology
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
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spelling E-Structures and almost regular poisson manifoldsGarmendia, AlfonsoMiranda Galcerán, Eva|||0000-0001-9518-5279Singular foliationsSymplectic structuresLie algebroidsPoisson groupoidsClassificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometryClassificació AMS::57 Manifolds and cell complexes::57R Differential topologyÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integralsIn recent years, b-symplectic manifolds have emerged as important objects in symplectic geometry. These manifolds are Poisson manifolds that exhibit symplectic behaviour away from a distinguished hypersurface, where the symplectic form degenerates in a controlled manner. Inspired by this rich landscape, E-structures were introduced by Nest and Tsygan in [NT01] as a comprehensive framework for exploring generalizations of b-structures. This paper initiates a deeper investigation into their Poisson facets, building on foundational work by [MS21]. We also examine the closely related concept of almost regular Poisson manifolds, as studied in [AZ17], which reveals a natural Poisson groupoid associated with these structures. In this article, we investigate the intricate relationship between E-structures and almost regular Poisson structures. Our comparative analysis not only scrutinizes their Poisson properties but also offers explicit formulae for the Poisson structure on the Poisson groupoid associated to the E-structures as both Poisson manifolds and singular foliations. In doing so, we reveal an interesting link between the existence of commutative frames and Darboux-Carathéodory-type expressions for the relevant structures.Peer Reviewed20262026-03-3020262026-04-13journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/460490https://dx.doi.org/10.1017/S1474748026101595reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:dnet:upcommonspor::59162ad4df80dca3e3e8fbf78a5ddcc12026-05-27T15:37:01Z
dc.title.none.fl_str_mv E-Structures and almost regular poisson manifolds
title E-Structures and almost regular poisson manifolds
spellingShingle E-Structures and almost regular poisson manifolds
Garmendia, Alfonso
Singular foliations
Symplectic structures
Lie algebroids
Poisson groupoids
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::57 Manifolds and cell complexes::57R Differential topology
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
title_short E-Structures and almost regular poisson manifolds
title_full E-Structures and almost regular poisson manifolds
title_fullStr E-Structures and almost regular poisson manifolds
title_full_unstemmed E-Structures and almost regular poisson manifolds
title_sort E-Structures and almost regular poisson manifolds
dc.creator.none.fl_str_mv Garmendia, Alfonso
Miranda Galcerán, Eva|||0000-0001-9518-5279
author Garmendia, Alfonso
author_facet Garmendia, Alfonso
Miranda Galcerán, Eva|||0000-0001-9518-5279
author_role author
author2 Miranda Galcerán, Eva|||0000-0001-9518-5279
author2_role author
dc.subject.none.fl_str_mv Singular foliations
Symplectic structures
Lie algebroids
Poisson groupoids
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::57 Manifolds and cell complexes::57R Differential topology
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
topic Singular foliations
Symplectic structures
Lie algebroids
Poisson groupoids
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::57 Manifolds and cell complexes::57R Differential topology
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
description In recent years, b-symplectic manifolds have emerged as important objects in symplectic geometry. These manifolds are Poisson manifolds that exhibit symplectic behaviour away from a distinguished hypersurface, where the symplectic form degenerates in a controlled manner. Inspired by this rich landscape, E-structures were introduced by Nest and Tsygan in [NT01] as a comprehensive framework for exploring generalizations of b-structures. This paper initiates a deeper investigation into their Poisson facets, building on foundational work by [MS21]. We also examine the closely related concept of almost regular Poisson manifolds, as studied in [AZ17], which reveals a natural Poisson groupoid associated with these structures. In this article, we investigate the intricate relationship between E-structures and almost regular Poisson structures. Our comparative analysis not only scrutinizes their Poisson properties but also offers explicit formulae for the Poisson structure on the Poisson groupoid associated to the E-structures as both Poisson manifolds and singular foliations. In doing so, we reveal an interesting link between the existence of commutative frames and Darboux-Carathéodory-type expressions for the relevant structures.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-03-30
2026
2026-04-13
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/460490
https://dx.doi.org/10.1017/S1474748026101595
url https://hdl.handle.net/2117/460490
https://dx.doi.org/10.1017/S1474748026101595
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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