Experimental Mathematics

Does the Jones polynomial detect unknottedness?

Oliver T. Dasbach and Stefan Hougardy

Abstract

There have been many attempts to settle the question whether there exist nontrivial knots with trivial Jones polynomial. In this paper we show that such a knot must have crossing number at least 18. Furthermore we give the number of prime alternating knots and an upper bound for the number of prime knots up to 17 crossings. We also compute the number of different HOMFLY, Jones and Alexander polynomials for knots up to 15 crossings.

Article information

Source
Experiment. Math., Volume 6, Issue 1 (1997), 51-56.

Dates
First available in Project Euclid: 13 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1047565283

Mathematical Reviews number (MathSciNet)
MR1464581

Zentralblatt MATH identifier
0883.57006

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Citation

Dasbach, Oliver T.; Hougardy, Stefan. Does the Jones polynomial detect unknottedness?. Experiment. Math. 6 (1997), no. 1, 51--56. https://projecteuclid.org/euclid.em/1047565283


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