Twisted Alexander polynomials of 2-bridge knots for parabolic representations

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.

Minor changes. To appear in Pacific Journal of Mathematics

References in corpus (3)

• On the AJ conjecture for knots
• Poincaré duality and degrees of twisted Alexander polynomials
• The universal character ring of some families of one-relator groups

Cited by in corpus (9)

• Three flavors of twisted invariants of knots
• Continuant, Chebyshev polynomials, and Riley polynomials
• Computing twisted Alexander polynomials for Montesinos links
• On the twisted Alexander polynomial for representations into SL_2(C)
• Introduction to twisted Alexander polynomials and related topics
• On left-orderability and cyclic branched coverings
• Volumes of double twist knot cone-manifolds
• Twisted Alexander polynomials of tunnel number one Montesinos knots
• Twisted Alexander polynomials on curves in character varieties of knot groups