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2014•Pacific Journal of MathematicsOpen access

Twisted Alexander polynomials of 2-bridge knots for parabolic representations

Takayuki Morifuji, Anh T. Tran

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Abstract

In this paper we show that the twisted Alexander polynomial associated to a parabolic representation determines fiberedness and genus of a wide class of 2-bridge knots.As a corollary we give an affirmative answer to a conjecture of Dunfield, Friedl and Jackson for infinitely many hyperbolic knots.

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What this paper is about

In this paper we show that the twisted Alexander polynomial associated to a parabolic representation determines fiberedness and genus of a wide class of 2-bridge knots.As a corollary we give an affirmative answer to a conjecture of Dunfield, Friedl and Jackson for infinitely many hyperbolic knots.

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Available abstract

In this paper we show that the twisted Alexander polynomial associated to a parabolic representation determines fiberedness and genus of a wide class of 2-bridge knots.As a corollary we give an affirmative answer to a conjecture of Dunfield, Friedl and Jackson for infinitely many hyperbolic knots.

Key concepts: Mathematics, Corollary, Conjecture, Genus, Bridge (graph theory), Pure mathematics, Representation (politics), Class (philosophy)

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