  We prove that every finitely presentable group G arises as the fundamental
group of an orientable 3-complex obtained from a hyperbolic link complement, by
coning each boundary torus of the link exterior to a distinct point. We define
the closed-link-genus, clg(G), of any finitely presentable group G, which
completely characterizes fundamental groups of closed orientable 3-manifolds:
clg(G)=0 if and only if G is the fundamental group of a closed orientable
3-manifold. Moreover clg(G) gives an upper bound for the concept `genus(G)' of
genus defined earlier by Aitchison and Reeves, and in turn is bounded by the
minimal number of relations among all finite presentations of G.
