A Dunfield--Gong 4-Sphere is Standard

Trevor Oliveira-Smith

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arXiv · 2603.23717

A Dunfield--Gong 4-Sphere is Standard

Trevor Oliveira-Smith

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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 $B^{4}$.

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Trevor Oliveira-Smith. 2026-03-24. A Dunfield--Gong 4-Sphere is Standard. https://arxiv.org/abs/2603.23717

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