Algebraic and Geometric Topology 4 (2004), paper no. 22, pages 439-472.

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

John Crisp, Bert Wiest

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^2y^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

AMS subject classification. Primary: 20F36, 05C25. Secondary: 05C25.

DOI: 10.2140/agt.2004.4.439

E-print: arXiv:math.GR/0303217

Submitted: 10 April 2003. Accepted: 20 May 2004. Published: 27 June 2004.

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John Crisp, Bert Wiest

Institut de Mathematiques de Bourgogne (IMB), UMR 5584 du CNRS
Universite de Bourgogne, 9 avenue Alain Savary, B.P. 47870
21078 Dijon cedex, France

IRMAR, UMR 6625 du CNRS, Campus de Beaulieu, Universite de Rennes 1
35042 Rennes, France

Email: jcrisp@u-bourgogne.fr, bertold.wiest@math.univ-rennes1.fr

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