  The correlation functions of supersymmetric gauge theories on a four-manifold
X can sometimes be expressed in terms of topological invariants of X. We show
how the existence of superconformal fixed points in the gauge theory can
provide nontrivial information about four-manifold topology. In particular, in
the example of gauge group SU(2) with one doublet hypermultiplet, we derive a
theorem relating classical topological invariants such as the Euler character
and signature to sum rules for Seiberg-Witten invariants.
