Twisted Alexander Polynomials of Hyperbolic Knots

@article{Dunfield2012TwistedAP,
  title={Twisted Alexander Polynomials of Hyperbolic Knots},
  author={N. Dunfield and S. Friedl and Nicholas Jackson},
  journal={Experimental Mathematics},
  year={2012},
  volume={21},
  pages={329 - 352}
}
  • N. Dunfield, S. Friedl, Nicholas Jackson
  • Published 2012
  • Computer Science, Mathematics
  • Experimental Mathematics
  • We study a twisted Alexander polynomial naturally associated to a hyperbolic knot in an integer homology 3-sphere via a lift of the holonomy representation to . It is an unambiguous symmetric Laurent polynomial whose coefficients lie in the trace field of the knot. It contains information about genus, fibering, and chirality, and moreover, is powerful enough to sometimes detect mutation. We calculated this invariant numerically for all 313 209 hyperbolic knots in S 3 with at most 15 crossings… CONTINUE READING
    Twisted Alexander polynomials on curves in character varieties of knot groups
    6
    Twisted Alexander polynomials and character varieties of links
    ON THE TWISTED ALEXANDER POLYNOMIAL FOR REPRESENTATIONS INTO SL2(ℂ)
    3
    Nontrivial twisted Alexander polynomials
    Twisted Alexander polynomials of twisted Whitehead links
    Non-acyclic SL2-representations of twist knots

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 117 REFERENCES
    Twisted Alexander polynomial and Reidemeister torsion
    105
    Twisted Alexander invariant and non-abelian Reidemeister torsion for hyperbolic three-dimensional manifolds with cusps
    8
    REMARKS ON THE A-POLYNOMIAL OF A KNOT
    66
    Arithmetic of hyperbolic 3-manifolds
    208