Initial data sets and the topology of closed three-manifolds in general relativity

It is discussed the interaction between the matter content of a closed physical space, associated with a generic gravitational configuration (i.e. without symmetries), and the topology of the underlying closed three-manifold S. It is shown that, within the context of the conformal approach to the initial-value problem, the presence of enough matter and radiation favours those topologies we expect, on heuristic grounds, to be actually encountered, namely the three-sphere topology, or the (S1xS2)-worm-hole topology. It is also argued that such topologies leave, as far as the field equations are concerned, more room to possible gravitational initial data sets