English

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