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

Abstract

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