The Hilden Double Coset Problem in Braid Groups
Geometric Topology
2024-07-22 v3 Group Theory
Abstract
In this paper we provide a solution to the double coset problem for the braid group modulo the Hilden subgroup This result demonstrates that, as in the case of braid closures, the Link Problem for plat closures is "stably equivalent" to a solvable algebraic problem. A particularly interesting feature of the proof is that, like Garside's solutions to the Word and Conjugacy Problems, it too relies on Garside's decomposition of braids in
Keywords
Cite
@article{arxiv.2401.02488,
title = {The Hilden Double Coset Problem in Braid Groups},
author = {Seth Hovland},
journal= {arXiv preprint arXiv:2401.02488},
year = {2024}
}
Comments
Lemma 3.4 on page 7 is incorrect. This is crucial to the argument. The problem that could not be fixed is if there are parts of hilden subgroup elements that contain parts of powers of the garside element