Three dimensions of knot coloring
Geometric Topology
2016-05-13 v2 History and Overview
Abstract
This survey article discusses three aspects of knot colorings. Fox colorings are assignments of labels to arcs, Dehn colorings are assignments of labels to regions, and Alexander-Briggs colorings assign labels to vertices. The labels are found among the integers modulo n. The choice of n depends upon the knot. Each type of coloring rules has an associated rule that must hold at each crossing. For the Alexander Briggs colorings, the rules hold around regions. The relationships among the colorings is explained.
Cite
@article{arxiv.1301.5378,
title = {Three dimensions of knot coloring},
author = {J. Scott Carter and Daniel S. Silver and Susan G. Williams},
journal= {arXiv preprint arXiv:1301.5378},
year = {2016}
}
Comments
Short article (13 pages, 8 figures), Figure 8 has been corrected. updated bibliography and doi added