Siebenmann-type cobordisms with borders and topology changes by quantum tunneling

Abstract

Siebenmann-type cobordisms are constructed to describe topology changes with the Seifert fibered homology spheres in in-and out-states. We study the problem of determining of topology-changing amplitudes for these quantum tunneling processes. The calculations are performed in the stationary phase approximation for Kodama wave functions. In this approximation the amplitudes are expressed in terms of Chern-Simons invariants of flat SU(2)-connections over the cobordism boundary components. The topology-change amplitudes found are factorized into the Kodama wave functions for the lens spaces. The results are compared with those for Fintushel-Stern-type cobordisms which have been previously investigated.