English

A Dunfield--Gong 4-Sphere is Standard

Geometric Topology 2026-03-26 v1

Abstract

In this paper, we standardize a homotopy 44-sphere constructed by Dunfield and Gong. As a corollary, we show that the 1818-crossing knot 18nh0000060118_{\text{nh}00000601}, which is not known to be ribbon, is slice in the standard 44-ball. Thus, 18nh0000060118_{\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 B4B^{4}.

Cite

@article{arxiv.2603.23717,
  title  = {A Dunfield--Gong 4-Sphere is Standard},
  author = {Trevor Oliveira-Smith},
  journal= {arXiv preprint arXiv:2603.23717},
  year   = {2026}
}

Comments

15 Pages, 10 Figures. Comments Welcome!

R2 v1 2026-07-01T11:36:21.138Z