On right-angled Artin groups without surface subgroups

Abstract

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'.