The Hilden Double Coset Problem in Braid Groups

2024/01/04 by Seth Hovland, Hovland, Seth
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2401.02488

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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