Knot group

In mathematics, a knot is an embedding of a circle into 3-dimensional Euclidean space. The knot group of a knot K is defined as the fundamental group of the knot complement of K in R³,

${\displaystyle \pi _{1}(\mathbb {R} ^{3}\setminus K).}$

Other conventions consider knots to be embedded in the 3-sphere, in which case the knot group is the fundamental group of its complement in ${\displaystyle S^{3}}$.