Table of Contents
ISRN Algebra
Volume 2011, Article ID 102029, 6 pages
Research Article

Combinatorial Methods for Detecting Surface Subgroups in Right-Angled Artin Groups

Lyman Briggs College, Michigan State University, W-32 Holmes Hall, East Lansing, MI 48825-1107, USA

Received 15 May 2011; Accepted 30 June 2011

Academic Editors: A. Facchini, D. Hernandez, and H. You

Copyright © 2011 Robert W. Bell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We give a short proof of the following theorem of Sang-hyun Kim: if 𝐴 ( Ξ“ ) is a right-angled Artin group with defining graph Ξ“ , then 𝐴 ( Ξ“ ) contains a hyperbolic surface subgroup if Ξ“ contains an induced subgraph 𝐢 𝑛 for some 𝑛 β‰₯ 5 , where 𝐢 𝑛 denotes the complement graph of an 𝑛 -cycle. Furthermore, we give a new proof of Kim's cocontraction theorem.