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2016•arXiv (Cornell University)Open access

Twisted Alexander polynomials and character varieties of links

Takayuki Morifuji, Anh T. Tran

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Abstract

In this paper we study the twisted Alexander polynomial from the viewpoint of the SL(2,C)-character variety of a link group. In particular, we discuss fibering and genus detecting problems of oriented links, and give some finiteness theorems which characterize fiberedness and the genus of an alternating link. Moreover 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.

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What this paper is about

In this paper we study the twisted Alexander polynomial from the viewpoint of the SL(2,C)-character variety of a link group. In particular, we discuss fibering and genus detecting problems of oriented links, and give some finiteness theorems which characterize fiberedness and the genus of an alternating link. Moreover 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.

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Available abstract

In this paper we study the twisted Alexander polynomial from the viewpoint of the SL(2,C)-character variety of a link group. In particular, we discuss fibering and genus detecting problems of oriented links, and give some finiteness theorems which characterize fiberedness and the genus of an alternating link. Moreover 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.

Key concepts: Conjecture, Mathematics, Torsion (gastropod), Character (mathematics), Variety (cybernetics), Genus, Pure mathematics, Alexander polynomial

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