Let be a complete hyperbolic 3-manifold of finite volume that admits a decomposition into right-angled ideal polyhedra. We show that has a deformation retraction that is a virtually special square complex, in the sense of Haglund and Wise and deduce that such manifolds are virtually fibered. We generalise a theorem of Haglund and Wise to the relatively hyperbolic setting and deduce that is LERF and that the geometrically finite subgroups of are virtual retracts. Examples of 3-manifolds admitting such a decomposition include augmented link complements. We classify the low-complexity augmented links and describe an infinite family with complements not commensurable to any 3-dimensional reflection orbifold.
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Eric Chesebro, Jason DeBlois, Henry Wilton, Some virtually special hyperbolic 3-manifold groups. Comment. Math. Helv. 87 (2012), no. 3, pp. 727–787DOI 10.4171/CMH/267