Volume 8, issue 2 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 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.

Keywords
right-angled Artin group, graph group, co-contraction, surface group
Mathematical Subject Classification 2000
Primary: 20F65, 20F36
Secondary: 05C25
References
Publication
Received: 4 January 2008
Accepted: 23 February 2008
Published: 3 June 2008
Authors
Sang-hyun Kim
Department of Mathematics
University of Texas
1 University Station C1200
Austin, TX 78712-0257
USA