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Conjugacy in Garside groups I: Cyclings, powers, and rigidity


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dc.creator Birman, Joan S. es
dc.creator Gebhardt, Volker es
dc.creator González-Meneses López, Juan es 2016-06-15T07:16:57Z 2016-06-15T07:16:57Z 2007
dc.identifier.citation Birman, J.S., Gebhardt, V. y González-Meneses López, J. (2007). Conjugacy in Garside groups I: cyclings, powers, and rigidity. Groups, Geometry, and Dynamics, 1 (3), 221-279.
dc.identifier.issn 1661-7207 es
dc.identifier.issn 1661-7215 es
dc.description.abstract In this paper a relation between iterated cyclings and iterated powers of elements in a Garside group is shown. This yields a characterization of elements in a Garside group having a rigid power, where ‘rigid’ means that the left normal form changes only in the obvious way under cycling and decycling. It is also shown that, given X in a Garside group, if some power X m is conjugate to a rigid element, then m can be bounded above by ||∆||3. In the particular case of braid groups {Bn, n ∈ N}, this implies that a pseudo-Anosov braid has a small power whose ultra summit set consists of rigid elements. This solves one of the problems in the way of a polynomial solution to the conjugacy decision problem (CDP) and the conjugacy search problem (CSP) in braid groups. In addition to proving the rigidity theorem, it will be shown how this paper fits into the authors’ program for finding a polynomial algorithm to the CDP/CSP, and what remains to be done. es
dc.description.sponsorship National Science Foundation (United States) es
dc.description.sponsorship Ministerio de Educación y Ciencia es
dc.description.sponsorship Fondo Europeo de Desarrollo Regional es
dc.format application/pdf es
dc.language.iso eng es
dc.publisher European Mathematical Society es
dc.relation.ispartof Groups, Geometry, and Dynamics, 1 (3), 221-279.
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri *
dc.subject Garside groups es
dc.subject conjugacy problem es
dc.subject ultra summit set es
dc.subject rigidity es
dc.subject stable ultra summit set es
dc.title Conjugacy in Garside groups I: Cyclings, powers, and rigidity es
dc.type info:eu-repo/semantics/article es
dc.type.version info:eu-repo/semantics/publishedVersion es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de álgebra es
dc.relation.projectID DMS-9973232 es
dc.relation.projectID 0405586 es
dc.relation.projectID MTM2004-07203-C02-01 es
dc.identifier.doi es
idus.format.extent 41 p. es
dc.journaltitle Groups, Geometry, and Dynamics es
dc.publication.volumen 1 es
dc.publication.issue 3 es
dc.publication.initialPage 221 es
dc.publication.endPage 279 es
dc.relation.publicationplace Zurich es
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