On the perturbative expansion of a quantum field theory around a   topological sector
  The idea of treating general relativistic theories in a perturbative expansion around a topological theory has been recently put forward in the quantum gravity literature. Here we investigate the viability of this idea, by applying it to conventional Yang--Mills theory on flat spacetime. We find that the expansion around the topological theory coincides with the usual expansion around the abelian theory, though the equivalence is non-trivial. In this context, the technique appears therefore to be viable, but not to bring particularly new insights. Some implications for gravity are discussed. 
Carlo Rovelli, Simone Speziale