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arXiv · 1106.5634

On the Kawauchi conjecture about the Conway polynomial of achiral knots

Nicola Ermotti·Cam Van Quach Hongler·Claude Weber
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Abstract

We give a counterexample to the Kawauchi conjecture on the Conway polynomial of achiral knots which asserts that the Conway polynomial $C(z)$ of an achiral knot satisfies the splitting property $C(z)=F(z)F(-z)$ for a polynomial $F(z)$ with integer coefficients. We show that the Bonahon-Siebenmann decomposition of an achiral and alternating knot is reflected in the Conway polynomial. More explicitly, the Kawauchi conjecture is true for quasi-arborescent knots and counterexamples in the class of alternating knots must be quasi-polyhedral.

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Nicola Ermotti, Cam Van Quach Hongler, Claude Weber. 2011-06-28. On the Kawauchi conjecture about the Conway polynomial of achiral knots. https://arxiv.org/abs/1106.5634

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