A Dunfield--Gong 4-Sphere is Standard
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915889213865984 |
|---|---|
| author | Oliveira-Smith, Trevor |
| author_facet | Oliveira-Smith, Trevor |
| contents | 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 $B^{4}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23717 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Dunfield--Gong 4-Sphere is Standard Oliveira-Smith, Trevor Geometric Topology 57R60 (Primary), 57R65, 57K10 (Secondary) 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 $B^{4}$. |
| title | A Dunfield--Gong 4-Sphere is Standard |
| topic | Geometric Topology 57R60 (Primary), 57R65, 57K10 (Secondary) |
| url | https://arxiv.org/abs/2603.23717 |