White-black graphs and right-angled hyperbolic handlebodies

Abstract

Abstract We prove a partial analog of Andreev’s theorem on compact hyperbolic polyhedra for irreducible, atoroidal, compact 3-manifolds with non-empty boundary. More precisely, for a 3-manifoldM with non-empty boundary, let Γ be a so called white-black graph in ᏮM; we characterize the conditions on Γ such that M admits a compact hyperbolic structure with Γ as the singular locus which is right-angled on each edge of Γ. In particular, our result applies to handlebodies.