Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 4, Number 1 (2004), 439-472.
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 surface group (given by the relation ) never embeds in a right-angled Artin group.
Algebr. Geom. Topol., Volume 4, Number 1 (2004), 439-472.
Received: 10 April 2003
Accepted: 20 May 2004
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F36: Braid groups; Artin groups 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]
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