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.
CitationGonzalez, J.; Ventura, E. Twisted conjugacy in braid groups. "Israel journal of mathematics", 07 Febrer 2014, vol. 201, núm. 1, p. 455-476.
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