Flat Connection Contribution to Topology Changing Amplitudes in an Ensemble of Seifert Fibered Homology Spheres

Abstract

The Fintushel-Stern pseudofree orbifolds are exploited to construct wave functions of universes created as a result of the interaction of cones on lens spaces. We also study the problem of the definition of topology changing amplitudes for tunneling topology changes, described by cobordisms with Seifert fibered homology sphere boundaries. It is demonstrated that such topology changes are accompanied by creation or annihilation of the lens spaces. The topology-changing amplitude calculations are carried out in the stationary phase approximation for Kodama wave functions. In this approximation the changing amplitudes factorize and they are expressed by means of Chern-Simons invariants of flat connections over Seifert fibered homology spheres and lens spaces.