Twisted conjugacy in braid groups

In this note we solve the twisted conjugacy problem for braid groups, i.e., we propose an algorithm which, given two braids u,v is an element of B-n and an automorphism phi is an element of Aut(B-n), decides whether v = (phi(x))(-1)-ux for some x is an element of B-n. As a corollary, we deduce that...

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Detalles Bibliográficos
Autores: Gonzalez Meneses, Juan, Ventura Capell, Enric|||0000-0003-3519-4135
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/24771
Acceso en línea:https://hdl.handle.net/2117/24771
https://dx.doi.org/10.1007/s11856-014-0032-4
Access Level:acceso abierto
Palabra clave:Group theory
Braid group
Twisted conjugacy
Grups, Teoria de
Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
Descripción
Sumario:In this note we solve the twisted conjugacy problem for braid groups, i.e., we propose an algorithm which, given two braids u,v is an element of B-n and an automorphism phi is an element of Aut(B-n), decides whether v = (phi(x))(-1)-ux for some x is an element of B-n. As a corollary, we deduce that each group of the form B-n x H, a semidirect product of the braid group B-n by a torsion-free hyperbolic group H, has solvable conjugacy problem.