Finite group actions on the moduli space of self-dual connections. I

Abstract

Let M be a smooth simply connected closed 4-manifold with positive definite intersection form, Suppose a finite group G acts smoothly on AI, Let π: E → M be the instanton number one quaternion line bundle over M with a smooth G-action such that π is an equivariant map, We first show that there exists a Baire set in the G-invariant metrics on M such that the moduli space, M G of G-invariant irreducible self-dual connections is a manifold, By utilizing the G-transversality theory of T. Petrie, we then identify cohomology obstructions to globally perturbing the full space M * of irreducible self-dual connections to a G-manifold when G = Z2 and the fixed point setof the Z2 action on M is a nonempty collection of isolated points and Riemann surfaces. © 1991 American Mathematical Society.