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-1#X-2 with b(2)(+)(X-i) > 0, i = 1, 2. In addition let X be symplectic and c(1)(X)(2) > 0 and b(2)(+)(X) > 3. If sigma is a free anti-symplectic involution on X then the Seiberg-Witten invariants on X/sigma vanish for all spine structures an X/sigma, and if eta is a free symplectic involution on X then the quotients X/sigma and X/eta are not diffeomorphic to each other.