Doubles of Gluck twists: A five-dimensional approach

Abstract

Using a 5-dimensional perspective, we balance algebraic and geometric handle cancellation to show that doubles of Gluck twists of certain 2-spheres embedded in the 4-sphere with two minima are standard. This includes all 2-spheres which are unions of ribbon discs, one of which has undisking number one. As an application, we produce new examples of Schoenflies balls not known to be standard.