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 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.

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References in corpus (2)

• Unknotting numbers of 2-spheres in the 4-sphere
• 0-concordance of knotted surfaces and Alexander ideals

Cited by in corpus (4)

• Gluck twists on concordant or homotopic spheres
• Constructions of homotopy 4-spheres by pochette surgery
• Pochette surgery of 4-sphere
• Gluck twist and unknotting of satellite $2$-knots