Spacetime Topology from Cosmic Strings and Foliations

One of the major difficulties in the mathematical representation of the gravitational field is that it is not generally possible to determine when two spacetime models are unique - this is known as the exotic smoothness problem. In this talk I will discuss how to completely enumerate the differentiable structures of a closed four-manifold using a branched covering of the four-sphere. This will allow us to avoid the problem of exotic smoothness, and construct a formally complete semiclassical partition function. This construction naturally includes cosmic strings and a unique specification of the topology of a codimension two foliation of the four-manifold via a redefinition of the geometric degrees of freedom. As a result of this construction, we propose that spacetime topology emerges as a result of symmetry breaking of the fundamental fields in the early universe.