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THE 2-BRIDGE KNOTS OF UP TO 16 CROSSINGS

DAVID DE WIT

Department of Mathematics, The University of Queensland, 4072, Brisbane, Australia

https://doi.org/10.1142/S021821650700566XCited by:4 (Source: Crossref)

Abstract

For any given number of crossings c, there exists a formula to determine the number of 2-bridge knots of c 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.

Keywords:

2-bridge knots

AMSC: 57M25

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