Invariants

Tue, 02 Jun 2026 16:04:48 +0200

A central problem in knot theory is determining when two knots, or more generally two links, are equivalent. Since a single knot or link can be represented in many different ways, mathematicians have introduced the notion of invariants. These are numbers or polynomials associated to a knot or link that remain unchanged when the knot is deformed without being cut or passed through itself. In a sense, invariants function as fingerprints, allowing one to compare different representations of the same underlying topological object. If two links have different values of a given invariant, then they cannot possibly be equivalent.

Topology on Disentangled

Invariants