Bergeron, Nicolas; Wise, Daniel T. A boundary criterion for cubulation. (English) Zbl 1279.20051 Am. J. Math. 134, No. 3, 843-859 (2012). Summary: We give a criterion in terms of the boundary for the existence of a proper cocompact action of a word-hyperbolic group on a 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 J. Kahn and V. Marković [Ann. Math. (2) 175, No. 3, 1127-1190 (2012; Zbl 1254.57014)], and I. Agol’s criterion [J. Topol. 1, No. 2, 269-284 (2008; Zbl 1148.57023)], we find that every subgroup separable closed hyperbolic 3-manifold is virtually fibered. Cited in 1 ReviewCited in 50 Documents MSC: 20F67 Hyperbolic groups and nonpositively curved groups 57M50 General geometric structures on low-dimensional manifolds 57M10 Covering spaces and low-dimensional topology 55R05 Fiber spaces in algebraic topology Keywords:cocompact actions on CAT(0) cube complexes; word-hyperbolic groups; lattices; hyperbolic 3-manifold groups; surface groups Citations:Zbl 1254.57014; Zbl 1148.57023 PDFBibTeX XMLCite \textit{N. Bergeron} and \textit{D. T. Wise}, Am. J. Math. 134, No. 3, 843--859 (2012; Zbl 1279.20051) Full Text: DOI arXiv