Groups, Geometry, and Dynamics

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Volume 4, Issue 2, 2010, pp. 275–307
DOI: 10.4171/GGD/84

Published online: 2010-02-21

On right-angled Artin groups without surface subgroups

Sang-hyun Kim[1]

(1) University of Texas at Austin, USA

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'.

Keywords: Right-angled Artin group, graph group, surface group, label-reading map

Kim Sang-hyun: On right-angled Artin groups without surface subgroups. Groups Geom. Dyn. 4 (2010), 275-307. doi: 10.4171/GGD/84