Double coset problem for parabolic subgroups of braid groups

2014/02/22 by Arkadius Kalka, Kalka, Arkadius, Mina Teicher +3
Mathematics · #20F36 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1402.5541

openalex publication_date 2014/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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