Smooth structures on symplectic 4-manifolds with finite fundamental groups

摘要

Let $overline{X}$ be a closed symplectic 4-manifold with a finite fundamental group. It is shown that the quotient manifold $X$ of a free involution on $overline{X}$ does not decompose to a connected sum $X = X_1 sharp X_2$ with both $b_2^+(X_i) > 0$, and that the quotient manifolds of free symplectic, anti-symplectic involution have respectively nontrivial, trivial Seiberg-Witten invariant.