Stable isotopy in four dimensions

Abstract

We construct infinite families of topologically isotopic, but smoothly distinct knotted spheres, in many simply connected 4-manifolds that become smoothly isotopic after stabilizing by connected summing with S 2 × S 2 , and as a consequence, analogous families of diffeomorphisms and metrics of positive scalar curvature for such 4-manifolds. We also construct families of smoothly distinct links, all of whose corresponding proper sublinks are smoothly isotopic, that become smoothly isotopic after stabilizing.