  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.
