Abelian and metabelian quotients of surface braid groups

TL;DR

This paper investigates the structure of abelian and metabelian quotients of surface braid groups, providing presentations and rigidity results based on fibrations, advancing understanding of their algebraic properties.

Contribution

It introduces explicit group presentations and proves rigidity results for these quotients, extending the algebraic understanding of surface braid groups.

Findings

Explicit presentations of abelian and metabelian quotients

Rigidity results for these quotients from fibrations

Enhanced understanding of surface braid group structures

Abstract

In this paper we study abelian and metabelian quotients of braid groups on oriented surfaces with boundary components. We provide group presentations and we prove rigidity results for these quotients arising from exact sequences related to (generalised) Fadell-Neuwirth fibrations.