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Recent developments in the understanding of N = 2 supersymmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining fourmanifold invariants by counting SU (2) instantons, one can define equivalent four-manifold invariants by counting solutions of a non-linear equation with an abelian gauge group. This is a "dual" equation in which the gauge group is the dual of the maximal torus of SU (2). The new viewpoint suggests many new results about the Donaldson invariants.
Edward Witten (Sat,) studied this question.