Gluck twist on a certain family of 2-knots

TL;DR

This paper demonstrates that applying the Gluck twist to a specific family of 2-knots results in the standard 4-sphere, using Kirby calculus techniques.

Contribution

It shows that certain Gluck twists on a family of 2-knots yield the standard 4-sphere, advancing understanding of 4-manifold topology.

Findings

Gluck twist on these 2-knots produces S^4

Kirby calculus is effective for this analysis

Identifies conditions under which the twist yields the standard sphere

Abstract

We show that by performing the Gluck twist along the 2-knot $K^2_{pq}$ derived from two ribbon presentations of the ribbon 1-knot $K(p,q)$ we get the standard 4-sphere $S^4$. In the proof we apply Kirby calculus.