## Algebraic & Geometric Topology

### 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 $x2y2=z2$) never embeds in a right-angled Artin group.

#### Article information

Source
Algebr. Geom. Topol., Volume 4, Number 1 (2004), 439-472.

Dates
Accepted: 20 May 2004
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.agt/1513882484

Digital Object Identifier
doi:10.2140/agt.2004.4.439

Mathematical Reviews number (MathSciNet)
MR2077673

Zentralblatt MATH identifier
1057.20028

#### Citation

Crisp, John; Wiest, Bert. Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups. Algebr. Geom. Topol. 4 (2004), no. 1, 439--472. doi:10.2140/agt.2004.4.439. https://projecteuclid.org/euclid.agt/1513882484

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