We consider the natural contraction from the central Haagerup tensor product of a *-algebra with itself to the space of completely bounded maps on and investigate those where there exists an inverse map with finite norm . We show that a stabilised version depends only on the primitive ideal space . The dependence is via simplicial complex structures (defined from primal intersections) on finite sets of primitive ideals that contain a Glimm ideal of . Moreover , with the compact operators, which requires us to develop the theory in the context of *-algebras that are not necessarily unital