A combination theorem for special cube complexes

We prove that certain compact cube complexes have special finite covers.This means they have finite covers whose fundamental groups are quasiconvex subgroups of right-angled Artin groups.As a result we obtain linearity and the separability of quasiconvex subgroups for the groups we consider.Our result applies, in particular, to a compact negatively curved cube complex whose hyperplanes do not self-intersect.For a cube complex with word-hyperbolic fundamental group, we show that it is virtually special if and only if its hyperplane stabilizers are separable.In a final application, we show that the fundamental groups of every simple type uniform arithmetic hyperbolic manifolds are cubical and virtually special.