Quadruple crossing number of knots and links
Geometric Topology
2019-02-20 v2
Abstract
A quadruple crossing is a crossing in a projection of a knot or link that has four strands of the knot passing straight through it. A quadruple crossing projection is a projection such that all of the crossings are quadruple crossings. In a previous paper, it was proved that every knot and link has a quadruple crossing projection and hence, every knot has a minimal quadruple crossing number. In this paper, we investigate quadruple crossing number, and in particular, use the span of the bracket polynomial to determine quadruple crossing number for a variety of knots and links.
Keywords
Cite
@article{arxiv.1211.2726,
title = {Quadruple crossing number of knots and links},
author = {Colin Adams},
journal= {arXiv preprint arXiv:1211.2726},
year = {2019}
}
Comments
11 pages, 7 figures, correction to one of the skein relations and addition to attributions in introduction