Baumslag-Solitar graphs through colours

TL;DR

This paper introduces Baumslag-Solitar graphs, a type of higher-rank graph, constructed via coloured graphs, providing a new perspective on higher-dimensional graph structures and their $C^*$-algebras.

Contribution

It presents a novel method of constructing Baumslag-Solitar graphs through coloured graphs, extending the understanding of higher-rank graphs using category theory.

Findings

Constructed Baumslag-Solitar graphs via coloured graphs.

Connected higher-rank graphs to $C^*$-algebras.

Extended the theory of higher-dimensional graph structures.

Abstract

Higher-rank graphs are, as the name suggests, higher-dimensional analogues of directed graphs which we will define using category theory. The whole idea of my project was to construct what we call a Baumslag-Solitar graph, a higher-rank graph. They're too abstract an idea to picture, but in building Baumslag-Solitar graphs through coloured graphs, we are able to do so. I modelled my work on constructing Baumslag-Solitar graphs off Hazlewood, Raeburn, Sims, and Webster's Remarks on some fundamental results about higher-rank graphs and their $C^*$-algebras. This was a novel approach in understanding the generalisation of directed graphs.