Determinant


The determinant of a knot is 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.


References

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