TOPOLOGY CHANGE IN (2+1)-DIMENSIONAL GRAVITY

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, the amplitude for a simple topology-changing process is evaluated. It is shown 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.