Volume 4, issue 1 (2004)

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Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups

John Crisp and Bert Wiest

Algebraic & Geometric Topology 4 (2004) 439–472
 arXiv: math.GR/0303217
Abstract

We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to right-angled Artin groups a result of Lyndon for free groups, we show that the Euler characteristic $-1$ surface group (given by the relation ${x}^{2}{y}^{2}={z}^{2}$) never embeds in a right-angled Artin group.

Keywords
cubed complex, graph braid group, graph group, right-angled Artin group, configuration space
Mathematical Subject Classification 2000
Primary: 20F36, 05C25
Secondary: 05C25