Double Centralizers of Parabolic Subgroups of Braid Groups
David Garber, Arkadius Kalka, Eran Liberman, Mina Teicher
TL;DR
This paper characterizes the double centralizer of parabolic subgroups in braid groups and offers a new, potentially more efficient method for solving the subgroup conjugacy problem, also providing insights into centralizers.
Contribution
It provides a complete characterization of double centralizers of parabolic subgroups and introduces an improved approach to the subgroup conjugacy problem in braid groups.
Findings
Double centralizer of parabolic subgroups characterized
New solution to subgroup conjugacy problem proposed
Centralizer of all parabolic subgroups characterized
Abstract
We characterize the double centralizer of all parabolic subgroups of the braid groups. We apply this result to provide a new and potentially more efficient solution to the subgroup conjugacy problem for parabolic subgroups. In the course of the proof we also characterize the centralizer for all parabolic subgroups.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology