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arXiv · 2412.14345

Coxeter-type quotients of surface braid groups

Renato Diniz·Oscar Ocampo·Paulo Cesar Cerqueira dos Santos Júnior
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Abstract

Let $M$ be a closed surface, $q\geq 2$ and $n\geq 2$. In this paper, we analyze the Coxeter-type quotient group $B_n(M)(q)$ of the surface braid group $B_{n}(M)$ by the normal closure of the element $σ_1^q$, where $σ_1$ is the classic Artin generator of the Artin braid group $B_n$. Also, we study the Coxeter-type quotient groups obtained by taking the quotient of $B_n(M)$ by the commutator subgroup of the respective pure braid group $[P_n(M),P_n(M)]$ and adding the relation $σ_1^q=1$, when $M$ is a closed orientable surface or the disk.

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BibTeXRIS

Renato Diniz, Oscar Ocampo, Paulo Cesar Cerqueira dos Santos Júnior. 2024-12-18. Coxeter-type quotients of surface braid groups. https://arxiv.org/abs/2412.14345

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