The mod 4 Kawauchi Conjecture
Prior state unknown→proved
the mod 4 form; the general conjecture is false by Ermotti, Hongler and Weber
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geometry-topology / Knot theory
The mod 4 Kawauchi Conjecture
Kawauchi conjectured that the Conway polynomial of an amphicheiral knot factors as $\nabla_K(z) = f(z)f(-z)$ for an integer polynomial $f$. Hartley proved it for negative amphicheiral knots and Ermotti, Hongler and Weber published the first counterexample to the general case. The mod 4 form of the conjecture, equivalent to a statement the author conjectured independently in 2006, is true.
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Kawauchi conjectured that the Conway polynomial of an amphicheiral knot factors as $\nabla_K(z) = f(z)f(-z)$ for an integer polynomial $f$. Hartley proved it for negative amphicheiral knots and Ermotti, Hongler and Weber published the first counterexample to the general case. The mod 4 form of the conjecture, equivalent to a statement the author conjectured independently in 2006, is true.
the mod 4 form; the general conjecture is false by Ermotti, Hongler and Weber
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