Reverse engineering small 4–manifolds

Abstract

We introduce a general procedure called ‘reverse engineering’ that can be used to construct infinite families of smooth $4$–manifolds in a given homeomorphism type. As one of the applications of this technique, we produce an infinite family of pairwise nondiffeomorphic $4$–manifolds homeomorphic to ${ℂ\mathbb{P}}^2\#3{\overline{ℂ\mathbb{P}}}^2$.