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 A note on indecomposable 4-manifolds Bull. Korean Math. Soc. 2005 Vol. 42, No. 4, 817-828 Published online December 1, 2005 Yong Seung Cho and Yoon Hi Hong Ewha Women's University, Ewha Women's University Abstract : In this note we show that there is an anti-symplectic involution $\sigma :X\to X$ on a simply-connected, closed, non-K\" ahler and symplectic 4-manifold $X$ with a disjoint union of Riemann surfaces $\amalg_{i=1}^n \Sigma_i, n\ge 2$ as a fixed point set. Also we show that its quotient $X/\sigma$ is homeomorphic to $\Bbb {CP}^2\sharp r\bar {\Bbb {CP}}^2$ but not diffeomorphic to $\Bbb {CP}^2\sharp r\bar {\Bbb {CP}}^2,$ $r=b_2^- (X/\sigma).$ Keywords : non-Kahler symplectic 4-manifold, anti-symplectic involution, Dolgachev surface, Seiberg-Witten invariant MSC numbers : 14J27, 14J28, 53D05, 57M12, 57M60, 57R20, 57R57 Full-Text :