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 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'.

29 pages, 14 figures. Proof of Lemma 3.6 is simplified; several typos are corrected

References in corpus (2)

• Co-contractions of Graphs and Right-angled Artin Groups
• Conjugacy classes of solutions to equations and inequations over hyperbolic groups