Finite group actions on 4-manifolds

Abstract

Let X be a closed, oriented, smooth 4-manifold with a finite fundamental group and with a non-vanishing Seiberg-Witten invariant. Let G be a finite group. If G acts smoothly and freely on X, then the quotient X/G cannot be decomposed as X^X-i with £^(X,) > 0, i = 1, 2. In addition let X be symplectic and C|(X) 2 > 0 and b^(X) > 3. If a is a free anti-symplectic involution on X then the Seiberg-Witten invariants on X/a vanish for all spin c structures on X/a, and if IJ is a free symplectic involution on X then the quotients X/a and X/rj are not diffeomorphic to each other.1991 Mathematics subject classification (Amen Math. Soc): primary 57R55,57N13, 57S17.