The determinant of a knot is the absolute value of det(V + Vt), where V is a Seifert matrix for the knot. Equivalently, this is | Δ(-1) |, where Δ(t) is the Alexander polynomial.

The determinant is equal to the order of the homology of the two-fold branched cover of the knot.


[1] Rolfsen, D., Knots and Links, AMS Chelsea Publishing, Providence (2003).

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