The fibered-knot coefficient conjecture for theta
The fibered-knot coefficient conjecture for theta
Let be a fibered knot, and let be the degree of its Alexander polynomial , meaning the highest power of . Consider the coefficient of in , which is a polynomial in .
Fibered-knot coefficient conjecture. This coefficient is an integer multiple of
The claim would provide a fast-to-compute fiberedness criterion and can be stronger than the Alexander condition. The authors state that they have no theoretical support for it, so it remains open.
Sources & referencesView supporting material
Primary source
Dror Bar-Natan and Roland van der Veen, “A Fast, Strong, Topologically Meaningful and Fun Knot Invariant”, arXiv:2509.18456 (2026).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
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