Topology and dynamics in classical and quantum gravity

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I am studying the interplay between topology and the dynamics of gravity of spacetimes in 3, 4 and more dimensions, both in the context of classical relativity and quantum theory. One fundamental question I would like to answer is, does our universe appear to be topologically simple because its initial quantum state made it that way or because the dynamics of general relativity force all topological structures behind black hole horizons? My earlier work on topological censorship shows small scale topological structures with nontrivial fundamental group are shrouded from outside observers in both physically reasonable, asymptotically flat and asymptotically anti de Sitter spacetimes. Thus part of the answer to this question indeed lies in the classical dynamics of topology. However, it cannot be the entire answer as the initial quantum state and quantum dynamics of gravity must produce a classical spacetime that is asymptotically flat or asymptotically anti de Sitter for topological censorship to hold.  Therefore, it is also key to understand the interplay between topology and the quantum dynamics of a fundamental theory that includes gravity. Thus the dynamics of topological structures is important to our understanding of our universe at both the highest energy scales as described by a fundamental quantum theory and the lowest as described by classical relativity. Furthermore, topology may prove to be a key tool in understanding these relationships, as it is insensitive to the detailed properties of the dynamics of the quantum theory. Therefore its effects may provide a universal guide to discovering the fundamental properties of the correct high energy theory.  I plan to continue research into the role topology plays in both classical relativity and in the current problems in fundamental quantum theories such as string theory and loop quantum gravity.