English

Baumslag-Solitar graphs through colours

Category Theory 2022-06-03 v1 Combinatorics

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 CC^*-algebras. This was a novel approach in understanding the generalisation of directed graphs.

Keywords

Cite

@article{arxiv.2206.01180,
  title  = {Baumslag-Solitar graphs through colours},
  author = {Katie Buchhorn},
  journal= {arXiv preprint arXiv:2206.01180},
  year   = {2022}
}

Comments

Not intended for publication

R2 v1 2026-06-24T11:37:29.066Z