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arXiv · 2410.13544

Subgroups of braid groups generated by Birman-Ko-Lee generators

Anya Nordskova·Michel Van den Bergh
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Abstract

We define a Young subgroup of the braid group as a subgroup generated by an arbitrary subset of the Birman-Ko-Lee generators. We give an intrinsic description of such subgroups which yields, in particular, an easy criterion to decide membership. We also give an algorithm to write an element of a Young subgroup as a product of the generators. Our methods are based on analyzing the Hurwitz action on tuples over free groups via a diagrammatic approach.

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Anya Nordskova, Michel Van den Bergh. 2024-10-17. Subgroups of braid groups generated by Birman-Ko-Lee generators. https://arxiv.org/abs/2410.13544

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