#### Volume 22, issue 2 (2022)

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Gluck twisting roll spun knots

### Patrick Naylor and Hannah R Schwartz

Algebraic & Geometric Topology 22 (2022) 973–990
##### 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 $m,n\in ℤ$. It follows as a corollary that an infinite collection of twisted doubles of Gompf’s infinite-order corks are standard.

##### Keywords
$4$–manifolds, Gluck twists, spun $2$–knots
##### Mathematical Subject Classification
Primary: 57M99, 57R60