# Determinant

The determinant of a knot is the absolute value of det(V + V^{t}), 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

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