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 surface group (given by the relation ) never embeds in a right-angled Artin group.
"Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups." Algebr. Geom. Topol. 4 (1) 439 - 472, 2004. https://doi.org/10.2140/agt.2004.4.439