We study the class N of graphs, the right-angled Artin groups defined on which do not contain closed hyperbolic surface subgroups. We prove that a presumably smaller class N' is closed under amalgamating along complete subgraphs, and also under adding bisimplicial edges. It follows that chordal graphs and chordal bipartite graphs belong to N'.
Cite this article
Sang-hyun Kim, On right-angled Artin groups without surface subgroups. Groups Geom. Dyn. 4 (2010), no. 2, pp. 275–307DOI 10.4171/GGD/84