Stoimenow's sign conjecture for amphicheiral Alexander polynomials

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Let KK be an amphicheiral knot, and let ΔK\Delta_K be its Alexander polynomial. Stoimenow's sign conjecture. The sign of the leading coefficient of ΔK\Delta_K is

(−1)max deg⁡ΔK.(-1)^{\operatorname{max\,deg}\Delta_K}.

The conjecture is presented alongside Stoimenow's square leading-coefficient conjecture and is motivated by the same theorem and classes of amphicheiral knots. The supplied text reports that the relevant conjectures are disproved by the paper's counterexamples.

References

Primary source

James Conant and Vajira Manathunga, “The Conway Polynomial and Amphicheiral Knots”, arXiv:1608.04453 (2016).

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