Hyperbolic torsion polynomials of pretzel knots

Takayuki Morifuji; Anh T. Tran

doi:10.1515/advgeom-2020-0017

Hyperbolic torsion polynomials of pretzel knots

Takayuki Morifuji, Anh T. Tran

Faculty of Economics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we explicitly calculate the highest degree term of the hyperbolic torsion polynomial of an infinite family of pretzel knots. This gives supporting evidence for a conjecture of Dunfield, Friedl and Jackson that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. The verification of the genus part of the conjecture for this family of knots also follows from the work of Agol and Dunfield [1] or Porti [19].

Original language	English
Pages (from-to)	265-272
Number of pages	8
Journal	Advances in Geometry
Volume	21
Issue number	2
DOIs	https://doi.org/10.1515/advgeom-2020-0017
Publication status	Published - 2021 Apr 1

Keywords

canonical component
Hyperbolic torsion polynomial
pretzel knot
twisted Alexander polynomial

ASJC Scopus subject areas

Geometry and Topology

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10.1515/advgeom-2020-0017

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abstract = "In this paper, we explicitly calculate the highest degree term of the hyperbolic torsion polynomial of an infinite family of pretzel knots. This gives supporting evidence for a conjecture of Dunfield, Friedl and Jackson that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. The verification of the genus part of the conjecture for this family of knots also follows from the work of Agol and Dunfield [1] or Porti [19]. ",

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AB - In this paper, we explicitly calculate the highest degree term of the hyperbolic torsion polynomial of an infinite family of pretzel knots. This gives supporting evidence for a conjecture of Dunfield, Friedl and Jackson that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. The verification of the genus part of the conjecture for this family of knots also follows from the work of Agol and Dunfield [1] or Porti [19].

KW - canonical component

KW - Hyperbolic torsion polynomial

KW - pretzel knot

KW - twisted Alexander polynomial

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JF - Advances in Geometry

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Hyperbolic torsion polynomials of pretzel knots

Abstract

Keywords

ASJC Scopus subject areas

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