MONOPOLES AND FOUR-MANIFOLDS

Recent developments in the understanding of N = 2 super-symmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining four-manifold 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.