# A boundary criterion for cubulation

@article{Bergeron2009ABC,
title={A boundary criterion for cubulation},
author={Nicolas Bergeron and Daniel T. Wise},
journal={American Journal of Mathematics},
year={2009},
volume={134},
pages={843 - 859}
}
• Published 25 August 2009
• Mathematics
• American Journal of Mathematics
We give a criterion in terms of the boundary for the existence of a proper cocompact action of a word-hyperbolic group on a ${\rm CAT}(0)$ cube complex. We describe applications towards lattices and hyperbolic 3-manifold groups. In particular, by combining the theory of special cube complexes, the surface subgroup result of Kahn-Markovic, and Agol's criterion, we find that every subgroup separable closed hyperbolic 3-manifold is virtually fibered.
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