On finite quotients of surface braid groups having order at most $127$

Abstract

Let ${\Sigma }_b$ be a compact Riemann surface of genus $b\ge 2$ and let ${\mathsf{P}}_2({\Sigma }_b)={\pi }_1({\Sigma }_b\times {\Sigma }_b-\Delta )$ be the corresponding pure braid group on two strands. A finite quotient $\phi :{\mathsf{P}}_2({\Sigma }_b)\to G$ is called "admissible" if $\phi$ does not factor through ${\pi }_1({\Sigma }_b\times {\Sigma }_b)$. In this work we classify all admissible quotients of ${\mathsf{P}}_2({\Sigma }_b)$ such that $|G|\le 127$.

Significantly shorter version. 13 pages, 2 figures