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Juan González-Meneses and Enric Ventura (2011)

# Twisted conjugacy in braid groups

arXiv:1104.5690.

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

20F10, Mathematics - Group Theory, 20F36

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