Coxeter-type quotients of surface braid groups

Abstract

Let $M$ be a closed surface, $q\ge 2$ and $n\ge 2$. 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 $\ddot{I}{ƒ}_1^q$, where $\ddot{I}{ƒ}_1$ 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 $\ddot{I}{ƒ}_1^q=1$, when $M$ is a closed orientable surface or the disk.

10 pages. All comments are welcome