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

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. AMS Classification 20F36, 05C25; 05C25 Keywords Cubed complex, graph braid group, graph group, right-angled Artin group, configuration space

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