Co-contractions of Graphs and Right-angled Artin Groups

Details Co-contractions of Graphs and Right-angled Artin Groups Co-contractions of Graphs and Right-angled Artin Groups

2006-11-19

arxiv.org/abs/math/0611588v1

Algebr. Geom. Topol. 2008 vol. 8 (2) pp. 849-868

Mathematics

Group Theory

18 pages, 8 figures

Scientific paper

We define an operation on finite graphs, called co-contraction. By showing that co-contraction of a graph induces an injective map between right-angled Artin groups, we exhibit a family of graphs, without any induced cycle of length at least 5, such that the right-angled Artin groups on those graphs contain hyperbolic surface groups. This gives the negative answer to a question raised by Gordon, Long and Reid.

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