Topology change in (2+1)-dimensional gravity

Abstract

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.