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

John Crisp; Bert Wiest

doi:10.2140/agt.2004.4.439

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arXiv · math/0303217

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

John Crisp·Bert Wiest

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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^2y^2=z^2) never embeds in a right-angled Artin group.

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John Crisp, Bert Wiest. 2004-07-03. Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups. https://doi.org/10.2140/agt.2004.4.439

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