Cyclic group actions on gauge theory

Abstract

Let p : E → X be an SU (2)-bundle over a simply connected smooth closed 4-manifold X with Chern number k = nk′. Let the cyclic group ℤn act on X and the bundle p : E → X such that p is a ℤn-map. We compute the dimension of the moduli space of the anti-self-dual connections on the quotient bundle E′ → X′. Relating the ℤn-invariant moduli space and the equivariant Donaldson polynomial invariant on E → X, we study the Donaldson polynomial invariant on the quotient bundle E′ → X′.