Twisted Alexander polynomials of hyperbolic links
Takayuki Morifuji, Anh T. Tran
TL;DR
This paper uses twisted Alexander polynomials to analyze fibering and genus detection in hyperbolic links, extending existing conjectures and confirming them for specific link families.
Contribution
It generalizes a conjecture on torsion polynomials from hyperbolic knots to links and verifies it for an infinite family of hyperbolic 2-bridge links.
Findings
Confirmed the conjecture for an infinite family of hyperbolic 2-bridge links
Extended the conjecture from hyperbolic knots to hyperbolic links
Analyzed the role of parabolic representations in link groups
Abstract
In this paper we apply the twisted Alexander polynomial to study the fibering and genus detecting problems for oriented links. In particular we generalize a conjecture of Dunfield, Friedl and Jackson on the torsion polynomial of hyperbolic knots to hyperbolic links, and confirm it for an infinite family of hyperbolic 2-bridge links. Moreover we consider a similar problem for parabolic representations of 2-bridge link groups.
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