Equivariant classification of bm-symplectic surfaces

Inspired by Arnold’s classification of local Poisson structures [1] in the plane using the hierarchy of singularities of smooth functions, we consider the problem of global classification of Poisson structures on surfaces. Among the wide class of Poisson structures, we consider the class of bm-Poiss...

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Autores: Miranda Galcerán, Eva|||0000-0001-9518-5279, Planas Bahí, Arnau|||0000-0003-0276-0794
Tipo de documento: artigo
Data de publicação:2018
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositório:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglês
OAI Identifier:oai:upcommons.upc.edu:2117/121250
Acesso em linha:https://hdl.handle.net/2117/121250
https://dx.doi.org/10.1134/S1560354718040019
Access Level:Acceso aberto
Palavra-chave:Topological manifolds
Poisson distribution
Geometry, Differencial
Moser path method
singularities
b-symplectic manifolds
group actions
Varietats topològiques
Geometria diferencial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Varietats topològiques
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
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oai_identifier_str oai:upcommons.upc.edu:2117/121250
network_acronym_str ES
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repository_id_str
spelling Equivariant classification of bm-symplectic surfacesMiranda Galcerán, Eva|||0000-0001-9518-5279Planas Bahí, Arnau|||0000-0003-0276-0794Topological manifoldsPoisson distributionGeometry, DifferencialMoser path methodsingularitiesb-symplectic manifoldsgroup actionsVarietats topològiquesGeometria diferencialÀrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Varietats topològiquesÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencialInspired by Arnold’s classification of local Poisson structures [1] in the plane using the hierarchy of singularities of smooth functions, we consider the problem of global classification of Poisson structures on surfaces. Among the wide class of Poisson structures, we consider the class of bm-Poisson structures which can be also visualized using differential forms with singularities as bm-symplectic structures. In this paper we extend the classification scheme in [24] for bm-symplectic surfaces to the equivariant setting. When the compact group is the group of deck-transformations of an orientable covering, this yields the classification of these objects for nonorientable surfaces. The paper also includes recipes to construct bm-symplectic structures on surfaces. The feasibility of such constructions depends on orientability and on the colorability of an associated graph. The desingularization technique in [10] is revisited for surfaces and the compatibility with this classification scheme is analyzed in detail.Peer ReviewedSpringer20182018-07-2420182018-09-18journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://hdl.handle.net/2117/121250https://dx.doi.org/10.1134/S1560354718040019reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1212502026-05-27T15:37:01Z
dc.title.none.fl_str_mv Equivariant classification of bm-symplectic surfaces
title Equivariant classification of bm-symplectic surfaces
spellingShingle Equivariant classification of bm-symplectic surfaces
Miranda Galcerán, Eva|||0000-0001-9518-5279
Topological manifolds
Poisson distribution
Geometry, Differencial
Moser path method
singularities
b-symplectic manifolds
group actions
Varietats topològiques
Geometria diferencial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Varietats topològiques
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
title_short Equivariant classification of bm-symplectic surfaces
title_full Equivariant classification of bm-symplectic surfaces
title_fullStr Equivariant classification of bm-symplectic surfaces
title_full_unstemmed Equivariant classification of bm-symplectic surfaces
title_sort Equivariant classification of bm-symplectic surfaces
dc.creator.none.fl_str_mv Miranda Galcerán, Eva|||0000-0001-9518-5279
Planas Bahí, Arnau|||0000-0003-0276-0794
author Miranda Galcerán, Eva|||0000-0001-9518-5279
author_facet Miranda Galcerán, Eva|||0000-0001-9518-5279
Planas Bahí, Arnau|||0000-0003-0276-0794
author_role author
author2 Planas Bahí, Arnau|||0000-0003-0276-0794
author2_role author
dc.subject.none.fl_str_mv Topological manifolds
Poisson distribution
Geometry, Differencial
Moser path method
singularities
b-symplectic manifolds
group actions
Varietats topològiques
Geometria diferencial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Varietats topològiques
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
topic Topological manifolds
Poisson distribution
Geometry, Differencial
Moser path method
singularities
b-symplectic manifolds
group actions
Varietats topològiques
Geometria diferencial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Varietats topològiques
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
description Inspired by Arnold’s classification of local Poisson structures [1] in the plane using the hierarchy of singularities of smooth functions, we consider the problem of global classification of Poisson structures on surfaces. Among the wide class of Poisson structures, we consider the class of bm-Poisson structures which can be also visualized using differential forms with singularities as bm-symplectic structures. In this paper we extend the classification scheme in [24] for bm-symplectic surfaces to the equivariant setting. When the compact group is the group of deck-transformations of an orientable covering, this yields the classification of these objects for nonorientable surfaces. The paper also includes recipes to construct bm-symplectic structures on surfaces. The feasibility of such constructions depends on orientability and on the colorability of an associated graph. The desingularization technique in [10] is revisited for surfaces and the compatibility with this classification scheme is analyzed in detail.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-07-24
2018
2018-09-18
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/2117/121250
https://dx.doi.org/10.1134/S1560354718040019
url https://hdl.handle.net/2117/121250
https://dx.doi.org/10.1134/S1560354718040019
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-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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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score 15.300719

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