Alexander Polynomial

The Alexander polynomial is a mathematical tool used in knot theory to distinguish different knots. It assigns a specific polynomial (a mathematical expression involving variables and coefficients) to each knot, capturing its essential properties. Think of it as a unique "fingerprint" for knots: if two knots have different Alexander polynomials, they are not the same knot. It helps mathematicians classify and analyze knots by translating their complex, tangled structures into a manageable algebraic form, providing insights into their shape and structure while remaining consistent under continuous deformations.