On right-angled Artin groups without surface subgroups

TL;DR

This paper investigates the class of right-angled Artin groups that lack surface subgroups, establishing closure properties and identifying specific graph classes that belong to this class.

Contribution

It introduces a potentially smaller class of graphs closed under certain operations and shows that chordal and chordal bipartite graphs are included.

Findings

Class N' is closed under amalgamation along complete subgraphs.

Class N' is closed under adding bisimplicial edges.

Chordal and chordal bipartite graphs belong to N'.

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'.