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Hyperbolic torsion polynomials of pretzel knots

Takayuki Morifuji EMAIL logo and Anh T. Tran
From the journal Advances in Geometry

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].

Funding statement: The first author was partially supported by JSPS KAKENHI Grant Number 17K05261. The second author was supported by a JSPS postdoctoral fellowship and a grant from the Simons Foundation (no. 354595 to AT) while writing this paper.

  1. Communicated by: K. Ono

References

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Received: 2018-06-26
Revised: 2019-09-14
Published Online: 2021-04-16
Published in Print: 2021-04-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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