A family of representations of braid groups on surfaces

TL;DR

This paper introduces a new family of braid group representations on surfaces, extending well-known linear representations like Burau and Lawrence-Krammer-Bigelow to more complex topological settings.

Contribution

It generalizes existing braid group representations from discs to surfaces, providing a broader framework for understanding braid group actions.

Findings

New family of surface braid group representations proposed

Extensions of Burau and Lawrence-Krammer-Bigelow representations

Potential applications in topological and algebraic studies of braids

Abstract

We propose a family of new representations of the braid groups on surfaces that extend linear representations of the braid groups on a disc such as the Burau representation and the Lawrence-Krammer-Bigelow representation.