Double coset problem for parabolic subgroups of braid groups

Abstract

We solve the double coset problem for all parabolic subgroups of braid groups. The solution provides an effective reduction of this problem to the simultaneous conjugacy problem, and resolves the ambiguity introduced by the center of the group via the double centralizer theorem. We also prove that the subgroup-restricted conjugacy problem is unsolvable in braid groups of at least 5 strands.

12 pages