Twisted conjugacy in braid groups

Abstract

In this note we solve the twisted conjugacy problem for braid groups, i.e. we propose an algorithm which, given two braids $u,v\in B_n$ and an automorphism $\varphi \in Aut(B_n)$, decides whether $v=(\varphi (x){)}^{-1}ux$ for some $x\in B_n$. As a corollary, we deduce that each group of the form $B_n⋊H$, a semidirect product of the braid group $B_n$ by a torsion-free hyperbolic group $H$, has solvable conjugacy problem.

References in corpus (1)

• Free-by-cyclic groups have solvable conjugacy problem

Cited by in corpus (1)

• Classification of symmetry groups for planar n-body choreographies