Twisted Alexander polynomials of $2$-bridge knots for parabolic representations

Takayuki Morifuji and Anh T. Tran

Vol. 269 (2014), No. 2, 433–451

DOI: 10.2140/pjm.2014.269.433

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.

Keywords

2-bridge knot, parabolic representation, twisted Alexander polynomial

Mathematical Subject Classification 2010

Primary: 57M27

Milestones

Received: 21 December 2012

Revised: 22 August 2013

Accepted: 23 September 2013

Published: 26 July 2014