Stoimenow's sign conjecture for amphicheiral Alexander polynomials

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 degΔK.(-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.

Sources & referencesView supporting material

Primary source

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

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