Co-contractions of graphs and right-angled Artin groups

Kim, Sang-hyun

doi:10.2140/agt.2008.8.849

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Co-contractions of graphs and right-angled Artin groups

Sang-hyun Kim

Algebraic & Geometric Topology 8 (2008) 849–868

DOI: 10.2140/agt.2008.8.849

Abstract

We define an operation on finite graphs, called co-contraction. Then we show that for any co-contraction $\hat{Γ}$ 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 $\hat{Γ}$ . 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

Volume 8, issue 2 (2008)