Open Access
January, 2019 Links with trivial $Q$-polynomial
J. Math. Soc. Japan 71(1): 19-42 (January, 2019). DOI: 10.2969/jmsj/77167716


The $Q$-polynomial is an invariant of the isotopy type of an unoriented link defined by Brandt, Lickorish, Millett, and Ho around 1985. It is shown that there exist infinitely many prime knots and links with trivial $Q$-polynomial, and so the $Q$-polynomial does not detect trivial links.


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Yasuyuki MIYAZAWA. "Links with trivial $Q$-polynomial." J. Math. Soc. Japan 71 (1) 19 - 42, January, 2019.


Received: 19 January 2017; Revised: 26 May 2017; Published: January, 2019
First available in Project Euclid: 4 October 2018

zbMATH: 07056556
MathSciNet: MR3909913
Digital Object Identifier: 10.2969/jmsj/77167716

Primary: 57M25
Secondary: 57M27

Keywords: $Q$-polynomial , trivial polynomial

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 1 • January, 2019
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