Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups. (Q1880639)

The authors 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 they point out some consequences of these embedding results. They 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, the authors 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.