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Juan González-Meneses and Enric Ventura (2011)

Twisted conjugacy in braid groups


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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