English

On 3-super bridge knots

Geometric Topology 2012-09-17 v1

Abstract

It is known that there are only finitely many knots with super bridge index 3. Jin and Jeon have provided a list of possible such candidates. However, they conjectured that the only knots with super bridge index 3 are trefoil and the figure eight knot. In this paper, we prove that the 525_2 knot and the 626_2 knot are also 3-super bridge knots by providing a polynomial representation of these knots in degree 6.6. This also answers a question asked by Durfee and O'Shea in their paper on polynomial knots: is there any 5-crossing knot in degree 6?

Keywords

Cite

@article{arxiv.1209.3119,
  title  = {On 3-super bridge knots},
  author = {Rama Mishra},
  journal= {arXiv preprint arXiv:1209.3119},
  year   = {2012}
}

Comments

11 pages, 7 figures

R2 v1 2026-06-21T22:04:54.873Z