Twisted Alexander polynomials of hyperbolic links

Takayuki Morifuji; Anh T. Tran

doi:10.4171/PRIMS/53-3-3

Twisted Alexander polynomials of hyperbolic links

Takayuki Morifuji, Anh T. Tran

Faculty of Economics

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

6 Citations (Scopus)

Abstract

In this paper we apply the twisted Alexander polynomial to study 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.

Original language	English
Pages (from-to)	395-418
Number of pages	24
Journal	Publications of the Research Institute for Mathematical Sciences
Volume	53
Issue number	3
DOIs	https://doi.org/10.4171/PRIMS/53-3-3
Publication status	Published - 2017

Keywords

Character variety
Double twist link
Hyperbolic link
Parabolic representation
Twisted Alexander polynomial

ASJC Scopus subject areas

Mathematics(all)

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10.4171/PRIMS/53-3-3

Cite this

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title = "Twisted Alexander polynomials of hyperbolic links",

abstract = "In this paper we apply the twisted Alexander polynomial to study 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.",

keywords = "Character variety, Double twist link, Hyperbolic link, Parabolic representation, Twisted Alexander polynomial",

author = "Takayuki Morifuji and Tran, {Anh T.}",

note = "Funding Information: The authors would like to thank Nathan Dunfield, Hiroshi Goda and Takahiro Kitayama for useful comments. The first author has been partially supported by JSPS KAKENHI (grant nos. 26400096, 17K05261). The second author has been partially supported by a grant from the Simons Foundation (#354595). Publisher Copyright: {\textcopyright} 2017 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.",

year = "2017",

doi = "10.4171/PRIMS/53-3-3",

language = "English",

volume = "53",

pages = "395--418",

journal = "Publications of the Research Institute for Mathematical Sciences",

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T1 - Twisted Alexander polynomials of hyperbolic links

AU - Morifuji, Takayuki

AU - Tran, Anh T.

N1 - Funding Information: The authors would like to thank Nathan Dunfield, Hiroshi Goda and Takahiro Kitayama for useful comments. The first author has been partially supported by JSPS KAKENHI (grant nos. 26400096, 17K05261). The second author has been partially supported by a grant from the Simons Foundation (#354595). Publisher Copyright: © 2017 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.

PY - 2017

Y1 - 2017

N2 - In this paper we apply the twisted Alexander polynomial to study 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.

AB - In this paper we apply the twisted Alexander polynomial to study 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.

KW - Character variety

KW - Double twist link

KW - Hyperbolic link

KW - Parabolic representation

KW - Twisted Alexander polynomial

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M3 - Article

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SN - 0034-5318

VL - 53

SP - 395

EP - 418

JO - Publications of the Research Institute for Mathematical Sciences

JF - Publications of the Research Institute for Mathematical Sciences

IS - 3

ER -

Twisted Alexander polynomials of hyperbolic links

Abstract

Keywords

ASJC Scopus subject areas

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