A symplectic manifold homeomorphic but not diffeomorphic to $\mathbb{C`P}\mskip-2mu^2 \mskip1mu\#\mskip2mu 3{\mskip2mu\overline{\mskip-2mu\mathbb{C`P}\mskip-3mu}\mskip1mu}^2$

Abstract

In this article we construct a minimal symplectic $4$–manifold and prove it is homeomorphic but not diffeomorphic to ${ℂ\mathbb{P}}^2\#3{\overline{ℂ\mathbb{P}}}^2$.