Some virtually special hyperbolic 3-manifold groups

Abstract. Let M be a complete hyperbolic 3-manifold of finite volume that admits a decomposition into right-angled ideal polyhedra. We show that M 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 hyper-bolic setting and deduce that pi1M is LERF and that the geometrically finite subgroups of pi1M 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 comple-ments not commensurable to any 3-dimensional reflection orbifold. 1