Rational blow-down along Wahl type plumbing trees of spheres

Abstract

In this article, we construct smooth 4–manifolds homeomorphic but not diffeomorphic to ${ℂ\mathbb{P}}^2\#k{\overline{ℂ\mathbb{P}}}^2$, for $k\in \left\{6,7,8,9\right\},$ using the technique of rational blow-down along Wahl type plumbing trees of spheres (see J Wahl, Smoothings of normal surface singularities, Topology 20 (1981) 219–246).