Reducible braids and Garside theory

We show that reducible braids which are, in a Garside-theoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a certain subset of its conjugacy class which we call the stabilized set of sliding...

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Detalles Bibliográficos
Autores: González-Meneses López, Juan, Wiest, Bert
Tipo de recurso: artículo
Estado:Versión publicada
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:11441/42251
Acceso en línea:http://hdl.handle.net/11441/42251
https://doi.org/10.2140/agt.2011.11.2971
Access Level:acceso abierto
Palabra clave:braid group
Garside group
Nielsen–Thurston classification
algorithm
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repository_id_str
spelling Reducible braids and Garside theoryGonzález-Meneses López, JuanWiest, Bertbraid groupGarside groupNielsen–Thurston classificationalgorithmWe show that reducible braids which are, in a Garside-theoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a certain subset of its conjugacy class which we call the stabilized set of sliding circuits, and if it is reducible, then its reducibility is geometrically obvious: it has a round or almost round reducing curve. Moreover, for any given braid, an element of its stabilized set of sliding circuits can be found using the well-known cyclic sliding operation. This leads to a polynomial time algorithm for deciding the NielsenThurston type of any braid, modulo one well-known conjecture on the speed of convergence of the cyclic sliding operation.Australian Research Council’s Discovery ProjectsMinisterio de Educación y CienciaFondo Europeo de Desarrollo RegionalGeometry & Topology PublicationsÁlgebra2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/42251https://doi.org/10.2140/agt.2011.11.2971reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésAlgebraic & Geometric Topology, 11 (5), 2971-3010.DP1094072MTM2007-66929P09-FQM-5112Coventryinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/422512026-06-17T12:51:07Z
dc.title.none.fl_str_mv Reducible braids and Garside theory
title Reducible braids and Garside theory
spellingShingle Reducible braids and Garside theory
González-Meneses López, Juan
braid group
Garside group
Nielsen–Thurston classification
algorithm
title_short Reducible braids and Garside theory
title_full Reducible braids and Garside theory
title_fullStr Reducible braids and Garside theory
title_full_unstemmed Reducible braids and Garside theory
title_sort Reducible braids and Garside theory
dc.creator.none.fl_str_mv González-Meneses López, Juan
Wiest, Bert
author González-Meneses López, Juan
author_facet González-Meneses López, Juan
Wiest, Bert
author_role author
author2 Wiest, Bert
author2_role author
dc.contributor.none.fl_str_mv Álgebra
dc.subject.none.fl_str_mv braid group
Garside group
Nielsen–Thurston classification
algorithm
topic braid group
Garside group
Nielsen–Thurston classification
algorithm
description We show that reducible braids which are, in a Garside-theoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a certain subset of its conjugacy class which we call the stabilized set of sliding circuits, and if it is reducible, then its reducibility is geometrically obvious: it has a round or almost round reducing curve. Moreover, for any given braid, an element of its stabilized set of sliding circuits can be found using the well-known cyclic sliding operation. This leads to a polynomial time algorithm for deciding the NielsenThurston type of any braid, modulo one well-known conjecture on the speed of convergence of the cyclic sliding operation.
publishDate 2011
dc.date.none.fl_str_mv 2011
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/11441/42251
https://doi.org/10.2140/agt.2011.11.2971
url http://hdl.handle.net/11441/42251
https://doi.org/10.2140/agt.2011.11.2971
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Algebraic & Geometric Topology, 11 (5), 2971-3010.
DP1094072
MTM2007-66929
P09-FQM-5112
Coventry
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 Geometry & Topology Publications
publisher.none.fl_str_mv Geometry & Topology Publications
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 15,300719

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