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A boundary criterion for cubulation
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 134, Number 3, June 2012
- pp. 843-859
- 10.1353/ajm.2012.0020
- Article
- Additional Information
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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.