Alexander polynomial

Summary

The Alexander polynomial is a knot invariant that assigns to each knot a Laurent polynomial with integer coefficients. It was the first polynomial knot invariant, found by James Waddell Alexander II in the 1920s. It can be computed from a Seifert matrix, from a knot diagram, or from the homology of the infinite cyclic cover of the knot complement. It detects many knots but not all; some nontrivial knots have Alexander polynomial $1$.