Coxeter-type quotients of surface braid groups
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910752211730432 |
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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 |