## Algebraic & Geometric Topology

### Co-contractions of graphs and right-angled Artin groups

Sang-hyun Kim

#### Abstract

We define an operation on finite graphs, called co-contraction. Then we show that for any co-contraction $Γ̂$ of a finite graph $Γ$, the right-angled Artin group on $Γ$ contains a subgroup which is isomorphic to the right-angled Artin group on $Γ̂$. As a corollary, we exhibit a family of graphs, without any induced cycle of length at least 5, such that the right-angled Artin groups on those graphs contain hyperbolic surface groups. This gives the negative answer to a question raised by Gordon, Long and Reid.

#### Article information

Source
Algebr. Geom. Topol., Volume 8, Number 2 (2008), 849-868.

Dates
Accepted: 23 February 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796846

Digital Object Identifier
doi:10.2140/agt.2008.8.849

Mathematical Reviews number (MathSciNet)
MR2443098

Zentralblatt MATH identifier
1143.20023

#### Citation

Kim, Sang-hyun. Co-contractions of graphs and right-angled Artin groups. Algebr. Geom. Topol. 8 (2008), no. 2, 849--868. doi:10.2140/agt.2008.8.849. https://projecteuclid.org/euclid.agt/1513796846

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