Basic results on braid groups

These are Lecture Notes of a course given by the author at the French-Spanish School Tresses in Pau, held in Pau (France) in October 2009. It is basically an introduction to distinct approaches and techniques that can be used to show results in braid groups. Using these techniques we provide several...

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Autor: González-Meneses López, Juan
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2011
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/48898
Acceso en línea:http://hdl.handle.net/11441/48898
https://doi.org/10.5802/ambp.293
Access Level:acceso abierto
Palabra clave:Braids
Lecture notes
Torsion-free
Presentation
Garside
Nielsen-Thurston theory
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spelling Basic results on braid groupsGonzález-Meneses López, JuanBraidsLecture notesTorsion-freePresentationGarsideNielsen-Thurston theoryThese are Lecture Notes of a course given by the author at the French-Spanish School Tresses in Pau, held in Pau (France) in October 2009. It is basically an introduction to distinct approaches and techniques that can be used to show results in braid groups. Using these techniques we provide several proofs of well known results in braid groups, namely the correctness of Artin’s presentation, that the braid group is torsion free, or that its center is generated by the full twist. We also recall some solutions of the word and conjugacy problems, and that roots of a braid are always conjugate. We also describe the centralizer of a given braid. Most proofs are classical ones, using modern terminology. I have chosen those which I find simpler or more beautiful.Cet article contient les notes d’un course donné par l’auteur à l’Ecole Franco-Espagnole Tresses in Pau, qui a eu lieu à Pau (France) en Octobre 2009. Il s’agit essentiellement d’une introduction aux différents points des vue et techniques qui peuvent étre utilises pour montrer des résultats dans les groupes de tresses. En utilisant ces techniques on montre quelques résultats bien connus dans les groupes de tresses, à savoir l’exactitude de la presentation d’Artin, le fait que les groupes de tresses sont sans torsion, ou que son centre est engendré par le full twist. On rappelle quelques solutions des problèmes du mot et de la conjugaison, et aussi que les racines d’une tresse sont toutes conjuguées. On décrit aussi le centralisateur d’une tresse donnée. La plupart des preuves sont classiques, en utilisant de la terminologie moderne. J’ai choisi celles qui je trouve plus simples ou plus jolies.Austrailan Research Council's DiscoveryMinisterio de Educación y CienciaMinisterio de Ciencia e InnovaciónJunta de AndalucíaFondo Europeo de Desarrollo RegionalUniversité Blaise PascalÁlgebraFQM218: Geometría Algebraica, Sistemas Diferenciales y Singularidades2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/48898https://doi.org/10.5802/ambp.293reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésAnnales mathématiques Blaise Pascal, 18 (1), 15-59.MTM2007-66929MTM2010-19355P09-FQM-5112http://ambp.cedram.org/cedram-bin/article/AMBP_2011__18_1_15_0.pdfinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/488982026-06-17T12:51:07Z
dc.title.none.fl_str_mv Basic results on braid groups
title Basic results on braid groups
spellingShingle Basic results on braid groups
González-Meneses López, Juan
Braids
Lecture notes
Torsion-free
Presentation
Garside
Nielsen-Thurston theory
title_short Basic results on braid groups
title_full Basic results on braid groups
title_fullStr Basic results on braid groups
title_full_unstemmed Basic results on braid groups
title_sort Basic results on braid groups
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: Geometría Algebraica, Sistemas Diferenciales y Singularidades
dc.subject.none.fl_str_mv Braids
Lecture notes
Torsion-free
Presentation
Garside
Nielsen-Thurston theory
topic Braids
Lecture notes
Torsion-free
Presentation
Garside
Nielsen-Thurston theory
description These are Lecture Notes of a course given by the author at the French-Spanish School Tresses in Pau, held in Pau (France) in October 2009. It is basically an introduction to distinct approaches and techniques that can be used to show results in braid groups. Using these techniques we provide several proofs of well known results in braid groups, namely the correctness of Artin’s presentation, that the braid group is torsion free, or that its center is generated by the full twist. We also recall some solutions of the word and conjugacy problems, and that roots of a braid are always conjugate. We also describe the centralizer of a given braid. Most proofs are classical ones, using modern terminology. I have chosen those which I find simpler or more beautiful.
publishDate 2011
dc.date.none.fl_str_mv 2011
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/11441/48898
https://doi.org/10.5802/ambp.293
url http://hdl.handle.net/11441/48898
https://doi.org/10.5802/ambp.293
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Annales mathématiques Blaise Pascal, 18 (1), 15-59.
MTM2007-66929
MTM2010-19355
P09-FQM-5112
http://ambp.cedram.org/cedram-bin/article/AMBP_2011__18_1_15_0.pdf
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 Université Blaise Pascal
publisher.none.fl_str_mv Université Blaise Pascal
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 15,198674

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