Gluck twisting roll spun knots

TL;DR

This paper proves that certain smooth 4-spheres obtained via Gluck twisting are standard, and as a consequence, some twisted doubles of Gompf's corks are also standard, advancing understanding of 4-manifold topology.

Contribution

It demonstrates that all Gluck twists on specific spun knots yield the standard 4-sphere, revealing new insights into the structure of 4-manifolds and corks.

Findings

Gluck twists on m-twist n-roll spun knots produce standard 4-spheres.

Infinite twisted doubles of Gompf's corks are standard.

Supports the conjecture that certain exotic structures are actually standard.

Abstract

We show that the smooth homotopy 4-sphere obtained by Gluck twisting the m-twist n-roll spin of any unknotting number one knot is diffeomorphic to the standard 4-sphere, for any pair of integers (m,n). It follows as a corollary that an infinite collection of twisted doubles of Gompf's infinite order corks are standard.