Algebraic & Geometric Topology

Co-contractions of graphs and right-angled Artin groups

Sang-hyun Kim

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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

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

Received: 4 January 2008
Accepted: 23 February 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F36: Braid groups; Artin groups
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]

right-angled Artin group graph group co-contraction surface group


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.

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