#### Volume 4, issue 1 (2004)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
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
##### Publication
Received: 10 April 2003
Accepted: 20 May 2004
Published: 27 June 2004
##### Authors
 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 France Bert Wiest IRMAR UMR 6625 du CNRS Campus de Beaulieu Université de Rennes 1 35042 Rennes France