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Abstract

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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### Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 843-859
Launched on MUSE
2012-05-31
Open Access
No

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