Gluck twisting roll spun knots

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 $m,n\in \mathbb{Z}$. It follows as a corollary that an infinite collection of twisted doubles of Gompf’s infinite-order corks are standard.