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

Crisp, John¹ ; Wiest, Bert²

¹Institut de Mathématiques de Bourgogne (IMB), UMR 5584 du CNRS, Université de Bourgogne, 9 avenue Alain Savary, B.P. 47870, 21078 Dijon Cedex, France
²IRMAR, UMR 6625 du CNRS, Campus de Beaulieu, Université de Rennes 1, 35042 Rennes, France

Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 439-472

Résumé

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.

Détail

DOI : 10.2140/agt.2004.4.439

Keywords: cubed complex, graph braid group, graph group, right-angled Artin group, configuration space

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