Alexander polynomial

The Alexander polynomial is an important invariant in the field of knot theory, which studies the properties of knots and links in three-dimensional space. It provides a way to distinguish between different knots and links. ### Definition For a given knot or link, the Alexander polynomial is constructed using a presentation of the knot or link's fundamental group. Specifically, it is derived from the first homology group of the knot complement, which can be computed using a Seifert surface.