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Cubulating graphs of free groups with cyclic edge groups
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 132, Number 5, October 2010
- pp. 1153-1188
- 10.1353/ajm.2010.0004
- Article
- Additional Information
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We prove that if $G$ is a group that splits as a finite graph of finitely
generated free groups with cyclic edge groups, and $G$ has no
non-Euclidean Baumslag-Solitar subgroups, then $G$ is the fundamental
group of a compact nonpositively curved cube complex. In addition, if $G$
is also word-hyperbolic (i.e., if $G$ contains no Baumslag-Solitar
subgroups of any type), we show that $G$ is linear (in fact, is a subgroup
of $SL_n(Z)$).