Tokyo Journal of Mathematics

A Calculation of the Hyperbolic Torsion Polynomial of a Pretzel Knot

Takayuki MORIFUJI

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Abstract

In this short note, we calculate the highest degree term of the hyperbolic torsion polynomial of a pretzel knot with three tangles. It gives a supporting evidence for a conjecture of Dunfield, Friedl and Jackson that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot.

Article information

Source
Tokyo J. Math., Volume 42, Number 1 (2019), 219-224.

Dates
First available in Project Euclid: 18 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1563436919

Mathematical Reviews number (MathSciNet)
MR3982055

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M05: Fundamental group, presentations, free differential calculus 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Citation

MORIFUJI, Takayuki. A Calculation of the Hyperbolic Torsion Polynomial of a Pretzel Knot. Tokyo J. Math. 42 (2019), no. 1, 219--224. https://projecteuclid.org/euclid.tjm/1563436919


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