On the $S$-equivalence for Genus One Knots
Geometric Topology
2026-05-26 v1
Abstract
In this paper, we construct a sequence of genus one knots that are both S-equivalent, yet can be distinguished by the Jones polynomial. This is related to the problem 1.6 in Kirby's problem list (K3).
Cite
@article{arxiv.2605.25309,
title = {On the $S$-equivalence for Genus One Knots},
author = {Ziyi Liu and Jun Wang},
journal= {arXiv preprint arXiv:2605.25309},
year = {2026}
}