Home / Publications / Preprints / Twisted conjugacy in braid groups

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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