The Hilden Double Coset Problem in Braid Groups

Seth Hovland

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arXiv · 2401.02488

The Hilden Double Coset Problem in Braid Groups

Seth Hovland

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Abstract

In this paper we provide a solution to the double coset problem for the braid group $B_n$ modulo the Hilden subgroup $H_n.$ 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 $B_n.$

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Seth Hovland. 2024-01-04. The Hilden Double Coset Problem in Braid Groups. https://arxiv.org/abs/2401.02488

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