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


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 x2y2 = z2) never embeds in a right-angled Artin group.

cubed complex, graph braid group, graph group, right-angled Artin group, configuration space
Mathematical Subject Classification 2000
Primary: 20F36, 05C25
Secondary: 05C25
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Received: 10 April 2003
Accepted: 20 May 2004
Published: 27 June 2004
John Crisp
Institut de Mathématiques de Bourgogne (IMB)
UMR 5584 du CNRS
Université de Bourgogne
9 avenue Alain Savary
B.P. 47870
21078 Dijon Cedex
Bert Wiest
UMR 6625 du CNRS
Campus de Beaulieu
Université de Rennes 1
35042 Rennes