Seven Knots and Knots in the Seven-Color Map

摘要

This paper offers two knotty instances of the number seven. The first offering is the remarkable fact, due to John Conway, that any embedding into three-dimensional space of the complete graph on seven nodes will have a knot in it and that this fact is intimately related to knots on the torus and the seven-color map on the torus. We discuss these matters in the first three sections of the paper. The second offering is the equally amazing fact that there are (up to mirror images) exactly seven knots with seven crossings. That is subject of the last section of the paper.