Ribbon numbers of 12-crossing knots
Geometric Topology
2024-09-20 v1
Abstract
The ribbon number of a knot is the minimum number of ribbon singularities among all ribbon disks bounded by that knot. In this paper, we build on the systematic treatment of this knot invariant initiated in recent work of Friedl, Misev, and Zupan. We show that the set of Alexander polynomials of knots with ribbon number at most four contains 56 polynomials, and we use this set to compute the ribbon numbers for many 12-crossing knots. We also study higher-genus ribbon numbers of knots, presenting some examples that exhibit interesting behavior and establishing that the success of the Alexander polynomial at controlling genus-0 ribbon numbers does not extend to higher genera.
Keywords
Cite
@article{arxiv.2409.12910,
title = {Ribbon numbers of 12-crossing knots},
author = {Xianhao An and Matthew Aronin and David Cates and Ansel Goh and Benjamin Kirn and Josh Krienke and Minyi Liang and Samuel Lowery and Ege Malkoc and Jeffrey Meier and Max Natonson and Veljko Radić and Yavuz Rodoplu and Bhaswati Saha and Evan Scott and Roman Simkins and Alexander Zupan},
journal= {arXiv preprint arXiv:2409.12910},
year = {2024}
}
Comments
32 pages, 12 figures, 7 tables,