  We investigate topology changing processes in the WKB approximation of four
dimensional quantum cosmology with a negative cosmological constant. As
Riemannian manifolds which describe quantum tunnelings of spacetime we consider
constant negative curvature solutions of the Einstein equation i.e. hyperbolic
geometries. Using four dimensional polytopes, we can explicitly construct
hyperbolic manifolds with topologically non-trivial boundaries which describe
topology changes. These instanton-like solutions are constructed out of
8-cell's, 16-cell's or 24-cell's and have several points at infinity called
cusps. The hyperbolic manifolds are non-compact because of the cusps but have
finite volumes. Then we evaluate topology change amplitudes in the WKB
approximation in terms of the volumes of these manifolds. We find that the more
complicated are the topology changes, the more likely are suppressed.
