FIXED-POINTS AND REDUCIBLES IN EQUIVARIANT GAUGE-THEORY

In this paper we prove two technical theorems about the equivariant mo duli space of ASD connections on a SU2 or SO3 bundle over a smooth ori ented four-manifold X which is equipped with a smooth and orientation preserving action of a finite group pi. The first theorem relates, in the case pi = Z/p and compact moduli spaces, the existence of a non em pty fixed set in the moduli space to the value of a certain Donaldson polynomial invariant. The second theorem gives a criterion under which one can avoid fixed reducible ASD connections by slightly varying the metric on X within the class of equivariant metrics.