Journal of the Mathematical Society of Japan

Links with trivial $Q$-polynomial


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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.

Article information

J. Math. Soc. Japan, Volume 71, Number 1 (2019), 19-42.

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

$Q$-polynomial trivial polynomial


MIYAZAWA, Yasuyuki. Links with trivial $Q$-polynomial. J. Math. Soc. Japan 71 (2019), no. 1, 19--42. doi:10.2969/jmsj/77167716.

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