AMPLITUDES FOR TOPOLOGY CHANGE IN TURAEV-VIRO THEORY

We investigate the Turaev-Viro invariant (partition function) for 3-ma nifolds with a boundary. In the framework of a TQFT, the partition fun ction Z(M; Sigma 1, Sigma 2) of such a manifold can be interpreted as a transition amplitude for topology change Sigma(1) --> Sigma(2) in 3D gravity. We show that for S-2 boundaries Z(M; S-2) factorizes into a term which contains the boundary dependence and another which depends only on the topology of the underlying manifold. For a general T-g bou ndary this factorization holds only in a particular case. We construct specific examples of partition functions for the 3-ball B-3, the cyli nder S-2 x 1 and the genus-1 handlebody H-1.