Cyclic group actions on gauge theory (Q1917368)

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