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

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.