Exotic smooth structures on small 4-manifolds

Let M be either \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{CP}^{2}\#3\overline{\mathbb{CP}}^{2}$\end{document} or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$3\mathbb{CP}^{2}\#5\overline{\mathbb{CP}}^{2}$\end{document}. We construct the first example of a simply-connected irreducible symplectic 4-manifold that is homeomorphic but not diffeomorphic to M.