On a conjecture of Dunfield, Friedl and Jackson. (English. French summary) Zbl 1253.57007
Summary: In this short note, we show that the twisted Alexander polynomial associated to a parabolic \(SL(2,\mathbb{C})\)-representation detects genus and fibering of twist knots. As a corollary, a conjecture of N. Dunfield, S. Friedl and N. Jackson [Twisted Alexander polynomials of hyperbolic knots, arXiv:1108.3045] is proved for hyperbolic twist knots.
MSC:
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
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