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

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

2003-03-18

arxiv.org/abs/math/0303217v2

Algebr. Geom. Topol. 4 (2004) 439-472

Mathematics

Group Theory

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-22.abs.html

Scientific paper

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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