On the structure of the centralizer of a braid

The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and direct products of mixed braid groups. Then we construct a generating set of the central...

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Detalles Bibliográficos
Autor: González-Meneses López, Juan
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2004
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/43116
Acceso en línea:http://hdl.handle.net/11441/43116
https://doi.org/10.1016/j.ansens.2004.04.002
Access Level:acceso abierto
Palabra clave:braid
centralizer
Nielsen-Thurston theory
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spelling On the structure of the centralizer of a braidGonzález-Meneses López, JuanbraidcentralizerNielsen-Thurston theoryThe mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and direct products of mixed braid groups. Then we construct a generating set of the centralizer of any braid on n strands, which has at most k(k+1) 2 elements if n = 2k, and at most k(k+3) 2 elements if n = 2k + 1. These bounds are shown to be sharp, due to work of N.V.Ivanov and of S.J.Lee. Finally, we describe how one can explicitly compute this generating set.Ministerio de Ciencia y TecnologíaFondo Europeo de Desarrollo RegionalElsevierÁlgebraFQM218: Geometria Algebraica, Sistemas Diferenciales y SingularidadesMinisterio de Ciencia y Tecnología (MCYT). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)2004info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/43116https://doi.org/10.1016/j.ansens.2004.04.002reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésAnnales Scientifiques de l’École Normale Supérieure, 37 (5), 729-757.BFM2001-3207http://dx.doi.org/10.1016/j.ansens.2004.04.002info:eu-repo/semantics/openAccessoai:idus.us.es:11441/431162026-06-17T12:51:07Z
dc.title.none.fl_str_mv On the structure of the centralizer of a braid
title On the structure of the centralizer of a braid
spellingShingle On the structure of the centralizer of a braid
González-Meneses López, Juan
braid
centralizer
Nielsen-Thurston theory
title_short On the structure of the centralizer of a braid
title_full On the structure of the centralizer of a braid
title_fullStr On the structure of the centralizer of a braid
title_full_unstemmed On the structure of the centralizer of a braid
title_sort On the structure of the centralizer of a braid
dc.creator.none.fl_str_mv González-Meneses López, Juan
author González-Meneses López, Juan
author_facet González-Meneses López, Juan
author_role author
dc.contributor.none.fl_str_mv Álgebra
FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
Ministerio de Ciencia y Tecnología (MCYT). España
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
dc.subject.none.fl_str_mv braid
centralizer
Nielsen-Thurston theory
topic braid
centralizer
Nielsen-Thurston theory
description The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and direct products of mixed braid groups. Then we construct a generating set of the centralizer of any braid on n strands, which has at most k(k+1) 2 elements if n = 2k, and at most k(k+3) 2 elements if n = 2k + 1. These bounds are shown to be sharp, due to work of N.V.Ivanov and of S.J.Lee. Finally, we describe how one can explicitly compute this generating set.
publishDate 2004
dc.date.none.fl_str_mv 2004
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/43116
https://doi.org/10.1016/j.ansens.2004.04.002
url http://hdl.handle.net/11441/43116
https://doi.org/10.1016/j.ansens.2004.04.002
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Annales Scientifiques de l’École Normale Supérieure, 37 (5), 729-757.
BFM2001-3207
http://dx.doi.org/10.1016/j.ansens.2004.04.002
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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