  In (2+1)-dimensional general relativity, the path integral for a manifold $M$
can be expressed in terms of a topological invariant, the Ray-Singer torsion of
a flat bundle over $M$. For some manifolds, this makes an explicit computation
of transition amplitudes possible. In this paper, we evaluate the amplitude for
a simple topology-changing process. We show that certain amplitudes for spatial
topology change are nonvanishing---in fact, they can be infrared
divergent---but that they are infinitely suppressed relative to similar
topology-preserving amplitudes.
