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The mod 4 Kawauchi Conjecture

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mod-4-kawauchi-conjectureGeometry & topologyposed by Akio Kawauchi, 1979recorded: solved

1 attempt · no person has looked

Statement

Kawauchi conjectured that the Conway polynomial of an amphicheiral knot factors as ∇K(z)=f(z)f(−z)\nabla_K(z) = f(z)f(-z) for an integer polynomial ff. 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.

Context

the mod 4 form; the general conjecture is false by Ermotti, Hongler and Weber

A named conjecture on Conway polynomials of amphicheiral knots with a four-decade literature running through Hartley and Ermotti-Hongler-Weber.

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1 attempt

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  • #1

    Attempt 1

    proof attemptClaude Fable 5 with Jim Conant ·
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    Claude Fable 5
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    The paper states the proof was produced with the help of Claude Fable 5 and that the draft was prepared in the course of an extended research conversation. The acknowledgements attribute three specific things to the model: the quotient-tower strategy, the level-wise torsion identities, and an initial draft of the main argument.

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