Knot group

In mathematics, a knot is an embedding of a circle into 3-dimensional Euclidean space.

This is because an equivalence between two knots is a self-homeomorphism of

that is isotopic to the identity and sends the first knot onto the second.

The abelianization of a knot group is always isomorphic to the infinite cyclic group Z; this follows because the abelianization agrees with the first homology group, which can be easily computed.

The knot group (or fundamental group of an oriented link in general) can be computed in the Wirtinger presentation by a relatively simple algorithm.