Orbifolds, Quantum Cosmology, and Nontrivial Topology

In order to include nontrivial spatial topologies in the problem of quantum creation of a universe, it seems to be necessary to generalize the sum over compact, smooth 4-manifolds to a sum over finite-volume, compact 4-orbifolds. We consider in detail the case of a 4-spherical orbifold with a cone-point singularity. This allows for the inclusion of a nontrivial topology in the semiclassical path integral approach to quantum cosmology, in the context of a Robertson-Walker minisuperspace.