Twisted Conjugacy in Braid Groups

  title={Twisted Conjugacy in Braid Groups},
  author={Juan Gonz{\'a}lez-Meneses and Enric Ventura},
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… CONTINUE READING