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arXiv · 2209.03860

Graph of groups decompositions of graph braid groups

Daniel Berlyne
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Abstract

We provide an explicit construction that allows one to easily decompose a graph braid group as a graph of groups. This allows us to compute the braid groups of a wide range of graphs, as well as providing two general criteria for a graph braid group to split as a non-trivial free product, answering two questions of Genevois. We also use this to distinguish certain right-angled Artin groups and graph braid groups. Additionally, we provide an explicit example of a graph braid group that is relatively hyperbolic, but is not hyperbolic relative to braid groups of proper subgraphs. This answers another question of Genevois in the negative.

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Daniel Berlyne. 2022-09-08. Graph of groups decompositions of graph braid groups. https://doi.org/10.1142/s0218196723500583

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