The conjecture that the Wada polynomial is the Alexander polynomial at t=1t=-1

For a knot, let the Wada polynomial and Alexander polynomial be the knot invariants defined from representations of its braid group by automorphisms of a free group. Specialization conjecture. The Wada polynomial is the specialization of the Alexander polynomial at t=1t=-1. This is suggested by the computed examples of torus knots and links, the figure eight knot, the square knot, and granny's knot. The source notes that a proof can be recovered from results of Tetsuya Ito, Wada, and Sakuma.

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Primary source

Vladimir Shpilrain, “Knot invariants from representations of braids by automorphisms of a free group”, arXiv:2505.22403 (2025).

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