Doubles of Gluck twists: a five dimensional approach

TL;DR

This paper introduces a five-dimensional approach to analyze doubles of Gluck twists, demonstrating their standardness in specific cases and producing new examples of Schoenflies balls.

Contribution

It presents a novel five-dimensional perspective combining algebraic and geometric handle cancellation techniques for Gluck twists.

Findings

Doubles of certain Gluck twists are shown to be standard.

New examples of Schoenflies balls are constructed.

The approach applies to 2-spheres with specific properties.

Abstract

Using a 5-dimensional perspective, we balance algebraic and geometric handle cancellation to show that doubles of Gluck twists of certain 2-spheres 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.