Topology change and monopole creation

Lorentzian cobordism is considered as a mechanism for topology change in quantum gravity. It is shown that the condition for a topological cobordism to admit an appropriate metric is different in even and odd dimensions. In odd dimensions such a metric exists if and only if the initial and final manifolds have the same Euler characteristic. This means that pair creation of Kaluza-Klein monopoles cannot occur via the mechanism considered. Possible implications of this result are discussed. Lorentzian cobordism in two dimensions is also analyzed briefly.