Baumslag-Solitar graphs through colours

Katie Buchhorn

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arXiv · 2206.01180

Baumslag-Solitar graphs through colours

Katie Buchhorn

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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.

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Katie Buchhorn. 2022-06-01. Baumslag-Solitar graphs through colours. https://arxiv.org/abs/2206.01180

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