Exotic smooth structures on 3CP2♯8CP¯2

Abstract

Motivated by Stipsicz and Szabó's exotic 4-manifolds with b2+ = 3 and b2− = 8, we construct a family of simply connected smooth 4-manifolds with b2+ = 3 and b2− = 8. As a corollary, we conclude that the topological 4-manifold 3 C P 2 ♯ 8 C P ¯ 2 admits infinitely many distinct smooth structures.