Journal of the Mathematical Society of Japan

Links with trivial $Q$-polynomial

Yasuyuki MIYAZAWA

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1538640044

Digital Object Identifier
doi:10.2969/jmsj/77167716

Mathematical Reviews number (MathSciNet)
MR3909913

Zentralblatt MATH identifier
07056556

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

Keywords
$Q$-polynomial trivial polynomial

Citation

MIYAZAWA, Yasuyuki. Links with trivial $Q$-polynomial. J. Math. Soc. Japan 71 (2019), no. 1, 19--42. doi:10.2969/jmsj/77167716. https://projecteuclid.org/euclid.jmsj/1538640044


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References

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