Gluck twisting roll spun knots

Naylor, Patrick; Schwartz, Hannah R

doi:10.2140/agt.2022.22.973

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Gluck twisting roll spun knots

Patrick Naylor and Hannah R Schwartz

Algebraic & Geometric Topology 22 (2022) 973–990

DOI: 10.2140/agt.2022.22.973

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

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

Volume 22, issue 2 (2022)