A Dunfield--Gong 4-Sphere is Standard

TL;DR

This paper standardizes a specific homotopy 4-sphere and demonstrates that a particular 18-crossing knot is slice in the standard 4-ball, providing insights into the Slice-Ribbon Conjecture and knot theory.

Contribution

It standardizes a Dunfield-Gong 4-sphere and shows the 18-crossing knot is slice, offering potential counterexamples to the Slice-Ribbon Conjecture.

Findings

The homotopy 4-sphere constructed by Dunfield and Gong is shown to be standard.

The 18-crossing knot 18_{nh00000601} is slice in the standard 4-ball.

The same knot bounds a fibered handle-ribbon disk in B^4.

Abstract

In this paper, we standardize a homotopy $4$-sphere constructed by Dunfield and Gong. As a corollary, we show that the $18$-crossing knot $18_{\text{nh}00000601}$, which is not known to be ribbon, is slice in the standard $4$-ball. Thus, $18_{\text{nh}00000601}$ serves as a potential counterexample to the Slice-Ribbon Conjecture. In addition, we show that the same knot bounds a fibered handle-ribbon disk in $B^{4}$.