A Tabulation of Ribbon Knots in Tangle Form
Geometric Topology
2018-03-06 v2
Abstract
It is known that there are 21 ribbon knots with 10 crossings or fewer. We show that for every ribbon knot, there exists a tangle that satisfies two properties associated with the knot. First, under a specific closure, the closed tangle is equivalent to its corresponding knot. Second, under a different closure, the closed tangle is equivalent to the unlink. For each of these 21 ribbon knots, we present a 4-strand tangle that satisfies these properties. We provide diagrams of these tangles and also express them in planar diagram notation.
Cite
@article{arxiv.1705.10291,
title = {A Tabulation of Ribbon Knots in Tangle Form},
author = {Andrey Boris Khesin},
journal= {arXiv preprint arXiv:1705.10291},
year = {2018}
}
Comments
12 pages, see page 11 for tangle diagrams, see page 12 for tangle information, and see page 9 for link to the table contents