Portal de Periódicos da CAPES

A boundary criterion for cubulation

2012; Johns Hopkins University Press; Volume: 134; Issue: 3 Linguagem: Inglês

10.1353/ajm.2012.0020

1080-6377

Nicolas Bergeron, Daniel T. Wise,

Advanced Combinatorial 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.