QUANTUM COSMOLOGY WITH NONTRIVIAL TOPOLOGY

Quantum creation of a universe with a nontrivial spatial topology is considered. Using the Euclidean functional integral prescription, we calculate the wave function of such a universe with cosmological constant and without matter. The minisuperspace path integral is calculated in the semiclassical approximation, and it is shown that in order to include the nontrivial topologies in the path integral approach to quantum cosmology, it seems necessary to generalize the sum over compact and smooth 4-manifolds to sum over finite-volume compact 4-orbifolds.