The 2-bridge knots of up to 16 crossings
Geometric Topology
2007-05-23 v2
Abstract
For any given number of crossings , there exists a formula to determine the number of 2-bridge knots of crossings, and indeed it is a simple matter to actually construct presentations of these knots. However, the determination of whether a given (prime) knot is a 2-bridge knot remains a nontrivial exercise, and we have no procedure to determine bridge numbers more generally. Herein, we identify the 2-bridge knots within the Hoste--Thistlethwaite--Weeks tables of prime knots of up to 16 crossings by an exhaustive search of a larger set of 2-bridge knots. As the unknot is the only knot with bridge number 1, this yields a lower bound of 3 for the bridge numbers of the remaining knots.
Cite
@article{arxiv.math/0409351,
title = {The 2-bridge knots of up to 16 crossings},
author = {David De Wit},
journal= {arXiv preprint arXiv:math/0409351},
year = {2007}
}