Does the topology of space fluctuate?

Evidence is presented that the singularities induced in causal Lorentzian spacetimes by changes in 3-space topology give rise to infinite particle and energy production under reasonable laws of quantum field propagation. In the case of the gravitational field, if 3-space is compact the total energy must vanish. A topological transition therefore induces a violent collapse that effectively aborts the transition, since the collapse mode is the only mode carrying the negative energy needed to compensate the associated infinite energy production. The existence of the Hamiltonian constraint of general relativity suggests that topological stability is a local property of the quantum theory that is maintained even when 3-space is noncompact.Supported in part by National Science Foundation Grant No. PHY-8318635.