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 . 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
References
Publication
Received: 13 October 2020
Revised: 25 February 2021
Accepted: 15 April 2021
Published: 3 August 2022
Authors
Patrick Naylor
Mathematics Department
Princeton University
Princeton, NJ
United States
https://patricknaylor.org
Hannah R Schwartz
Mathematics Department
Princeton University
Princeton, NJ
United States