Dunfield, Friedl and Jackson's twisted Alexander polynomial conjecture for hyperbolic knots
Dunfield, Friedl and Jackson's twisted Alexander polynomial conjecture for hyperbolic knots
Let be a hyperbolic knot, let denote its genus, and let be a lift of the discrete and faithful representation defining the hyperbolic metric. Dunfield, Friedl and Jackson's conjecture. The twisted Alexander polynomial satisfies
Furthermore, is fibered if and only if is monic. This relates the holonomy twisted Alexander polynomial to the genus and proposes that it detects fibredness for hyperbolic knots; the supplied source does not indicate whether the assertion has been resolved.
Sources & referencesView supporting material
Primary source
Haimiao Chen, “Computing twisted Alexander polynomials for Montesinos links”, arXiv:1709.03116 (2021).
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