Dunfield–Friedl–Jackson conjecture for hyperbolic knots
Dunfield–Friedl–Jackson conjecture for hyperbolic knots
Let be a hyperbolic knot in , let be its exterior, and let denote its Thurston norm, equivalently
Let be a lift of the holonomy representation of to , and let be the associated -torsion polynomial. Dunfield–Friedl–Jackson conjecture.
and the exterior fibers over the circle if and only if is monic. The degree equality would sharpen the known torsion lower bound for the Thurston norm, while the monicity criterion predicts that the torsion polynomial detects fiberedness. It is known computationally for all hyperbolic knots with at most 15 crossings, but remains a conjecture in general.
Sources & referencesView supporting material
Primary source
Nathan M. Dunfield, Stavros Garoufalidis and Seokbeom Yoon, “1-loop equals torsion for fibered 3-manifolds”, arXiv:2304.00469 (2024).
Additional references
9 papers in this index state this conjecture (2013–2023). The statement above is taken from the most recent of them; the others are arXiv:2203.03239, arXiv:2108.08645, arXiv:1606.06360, arXiv:1511.00400, arXiv:1510.03216, arXiv:1412.4483, arXiv:1406.4626, arXiv:1301.1447.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.