Small exotic 4–manifolds

Abstract

In this article, we construct the first example of a simply-connected minimal symplectic 4–manifold that is homeomorphic but not diffeomorphic to $3{ℂ\mathbb{P}}^2\#7{\overline{ℂ\mathbb{P}}}^2$. We also construct the first exotic minimal symplectic ${ℂ\mathbb{P}}^2\#5{\overline{ℂ\mathbb{P}}}^2$.