English

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).

Keywords

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}
}