Volume 8, issue 2 (2008)

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Co-contractions of graphs and right-angled Artin groups

Sang-hyun Kim

Algebraic & Geometric Topology 8 (2008) 849–868
Abstract

We define an operation on finite graphs, called co-contraction. Then we show that for any co-contraction $\stackrel{̂}{\Gamma }$ of a finite graph $\Gamma$, the right-angled Artin group on $\Gamma$ contains a subgroup which is isomorphic to the right-angled Artin group on $\stackrel{̂}{\Gamma }$. 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.

Keywords
right-angled Artin group, graph group, co-contraction, surface group
Mathematical Subject Classification 2000
Primary: 20F65, 20F36
Secondary: 05C25