Presentations of braid groups of type $A$ arising from $(m+2)$-angulations of regular polygons

TL;DR

This paper explores new geometric presentations of type A braid groups derived from colored quivers and generalized polygon triangulations, linking algebraic structures with combinatorial geometry.

Contribution

It introduces a novel geometric interpretation of braid groups of type A via generalized triangulations of polygons, based on colored quivers of mutation type A.

Findings

Presentations of braid groups from colored quivers of mutation type A.

Geometric interpretation as generalized polygon triangulations.

Connection between algebraic and combinatorial structures.

Abstract

We describe presentations of braid groups of type $A$ arising from coloured quivers of mutation type $A$. We show that these can be interpreted geometrically as generalised triangulations of regular polygons.