Grid diagrams for higher-dimensional Thompson’s groups

We describe standard forms for elements of the higher-dimensional Thompson groups nV arising from gridding subdivision processes. These processes lead to standard normal form descriptions for elements in these groups, and sizes of these standard forms estimate the word length with respect to finite...

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Detalles Bibliográficos
Autores: Burillo Puig, José|||0000-0002-1078-3614, Cleary, Sean, Nucinkis, Brita
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::8243779b2427bf57958571528088fb49
Acceso en línea:https://hdl.handle.net/2117/462256
https://dx.doi.org/10.1017/S0305004126102047
Access Level:acceso abierto
Palabra clave:Finite groups
Infinite groups
Geometric group theory
Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups
Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
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spelling Grid diagrams for higher-dimensional Thompson’s groupsBurillo Puig, José|||0000-0002-1078-3614Cleary, SeanNucinkis, BritaFinite groupsInfinite groupsGeometric group theoryClassificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groupsClassificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groupsÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grupsWe describe standard forms for elements of the higher-dimensional Thompson groups nV arising from gridding subdivision processes. These processes lead to standard normal form descriptions for elements in these groups, and sizes of these standard forms estimate the word length with respect to finite generating sets. These gridded forms lead to standard algebraic descriptions as well, with respect to the both infinite and finite generating sets for these groups.Peer Reviewed20262026-01-0120262026-05-20journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/462256https://dx.doi.org/10.1017/S0305004126102047reponame: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::8243779b2427bf57958571528088fb492026-05-27T15:37:01Z
dc.title.none.fl_str_mv Grid diagrams for higher-dimensional Thompson’s groups
title Grid diagrams for higher-dimensional Thompson’s groups
spellingShingle Grid diagrams for higher-dimensional Thompson’s groups
Burillo Puig, José|||0000-0002-1078-3614
Finite groups
Infinite groups
Geometric group theory
Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups
Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
title_short Grid diagrams for higher-dimensional Thompson’s groups
title_full Grid diagrams for higher-dimensional Thompson’s groups
title_fullStr Grid diagrams for higher-dimensional Thompson’s groups
title_full_unstemmed Grid diagrams for higher-dimensional Thompson’s groups
title_sort Grid diagrams for higher-dimensional Thompson’s groups
dc.creator.none.fl_str_mv Burillo Puig, José|||0000-0002-1078-3614
Cleary, Sean
Nucinkis, Brita
author Burillo Puig, José|||0000-0002-1078-3614
author_facet Burillo Puig, José|||0000-0002-1078-3614
Cleary, Sean
Nucinkis, Brita
author_role author
author2 Cleary, Sean
Nucinkis, Brita
author2_role author
author
dc.subject.none.fl_str_mv Finite groups
Infinite groups
Geometric group theory
Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups
Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
topic Finite groups
Infinite groups
Geometric group theory
Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups
Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
description We describe standard forms for elements of the higher-dimensional Thompson groups nV arising from gridding subdivision processes. These processes lead to standard normal form descriptions for elements in these groups, and sizes of these standard forms estimate the word length with respect to finite generating sets. These gridded forms lead to standard algebraic descriptions as well, with respect to the both infinite and finite generating sets for these groups.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-01-01
2026
2026-05-20
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/2117/462256
https://dx.doi.org/10.1017/S0305004126102047
url https://hdl.handle.net/2117/462256
https://dx.doi.org/10.1017/S0305004126102047
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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score 15,812429

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