A VANISHING THEOREM FOR DONALDSON INVARIANTS

Given a smooth simply connected 4-manifold M, we prove that if there i s a smoothly embedded 2-torus T inside M, then the SU(2)-Donaldson inv ariants of M vanish on collections of 2-homology classes, ah of which are orthogonal to [T] and at least two of which are multiples of [T]. From this we deduce obstructions to the representability of 2-homology classes of some algebraic surfaces by smoothly embedded tori, and we compute the group of self-diffeomorphisms of certain 4-manifolds with boundary.