  We explicitly calculate the Green functions describing quantum changes of
topology in Friedman-Lemaitre-Robertson-Walker Universes whose spacelike
sections are compact but endowed with distinct topologies. The calculations are
performed using the long wavelength approximation at second order in the
gradient expansion. We argue that complex metrics are necessary in order to
obtain a non-vanishing Green functions and interpret this fact as demonstrating
that a quantum topology change can be viewed as a quantum tunneling effect. We
demonstrate that quantum topological transitions between curved hypersurfaces
are allowed whereas no transition to or from a flat section is possible,
establishing thus a selection rule. We also show that the quantum topology
changes in the direction of negatively curved hypersurfaces are strongly
enhanced as time goes on, while transitions in the opposite direction are
suppressed.
