Opened Access Twisted conjugacy in braid groups

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Author: González-Meneses López, Juan
Ventura Capell, Enric
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2014
Published in: Israel Journal of Mathematics, 201(1), 455-476
Document type: Article
Abstract: In this note we solve the twisted conjugacy problem for braid groups, i.e. we propose an algorithm which, given two braids u, v ∈ Bn and an automorphism ϕ ∈ Aut(Bn), decides whether v = (ϕ(x))−1ux for some x ∈ Bn. As a corollary, we deduce that each group of the form Bn o H, a semidirect product of the braid group Bn by a torsion-free hyperbolic group H, has solvable conjugacy problem.
Cite: González-Meneses López, J. y Ventura Capell, E. (2014). Twisted conjugacy in braid groups. Israel Journal of Mathematics, 201 (1), 455-476.
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