ANTI-SYMPLECTIC INVOLUTIONS ON NON-KÄHLER SYMPLECTIC 4-MANIFOLDS

In this note we construct an anti-symplectic involution on the non- $K\ddot{a}hler$ , symplectic 4-manifold which is constructed by Thurston and show that the quotient of the Thurston's 4-manifold is not symplectic. Also we construct a non- $K\ddot{a}hler$ , symplectic 4-manifold using the Gomph's symplectic sum method and an anti-symplectic involution on the non- $K\ddot{a}hler$ , symplectic 4-manifold.