Coxeter-type quotients of surface braid groups

Fuente: arXiv
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Autores principales: Diniz, Renato, Ocampo, Oscar, Júnior, Paulo Cesar Cerqueira dos Santos
Formato: Preprint
Publicado: 2024
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author Diniz, Renato
Ocampo, Oscar
Júnior, Paulo Cesar Cerqueira dos Santos
author_facet Diniz, Renato
Ocampo, Oscar
Júnior, Paulo Cesar Cerqueira dos Santos
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_14345
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Coxeter-type quotients of surface braid groups
Diniz, Renato
Ocampo, Oscar
Júnior, Paulo Cesar Cerqueira dos Santos
Group Theory
Geometric Topology
20F36, 20F05
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.
title Coxeter-type quotients of surface braid groups
topic Group Theory
Geometric Topology
20F36, 20F05
url https://arxiv.org/abs/2412.14345