Algebraic & Geometric Topology

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

John Crisp and Bert Wiest

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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.

Article information

Algebr. Geom. Topol., Volume 4, Number 1 (2004), 439-472.

Received: 10 April 2003
Accepted: 20 May 2004
First available in Project Euclid: 21 December 2017

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Zentralblatt MATH identifier

Primary: 20F36: Braid groups; Artin groups 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]

cubed complex graph braid group graph group right-angled Artin group configuration space


Crisp, John; Wiest, Bert. Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups. Algebr. Geom. Topol. 4 (2004), no. 1, 439--472. doi:10.2140/agt.2004.4.439.

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