The first 1,701,936 knots
The history of knot tabulation is long established, having begun over 120 years ago. In many ways, the compilations of the first knot tables marked the beginning of the modern study of knots, and it is perhaps not surprising that as knot theory and topology grew, so did the knot tables. Over the last few years, we have extended the tables to include all prime knots with 16 or fewer crossings. This represents more than a 130-fold increase in the number of tabulated knots since the last burst of tabulation that took place in the early 1980s. With more than 1.7 million knots now in the tables, we hope that the census will serve as a rich source of examples and counterexamples and as a general testing ground for our collective intuition. To this end, we have written a UNIX-based computer program called KnotScape which allows easy access to the tables. Obviously, we now have a great deal of data, and reporting on every aspect of the tabulated knots is not possible. Instead, in the first of three appendices we present a statistical summary of the census. The second appendix contains lists of hyperbolic knots with selected symmetries, and the final appendix contains brief descriptions of KnotScape and Weeks's program SnapPea which figures prominently in our work. We describe the hardware and software requirements of these programs, where to obtain them, and their capabilities.
scientific article; zbMATH DE number 1279095
scientific article