Knot group

From Topospaces
Jump to: navigation, search

This article describes a knot invariant

Definition

The knot group of a knot K (where K is a homeomorphic copy of S^1 inside S^3) is the fundamental group of the knot complement, viz., \pi_1(S^3 \setminus K). Note that S^3 \setminus K is path-connected, and its first homology group is \mathbb{Z}. Thus the Abelianization of the knot group is \mathbb{Z}. Further information: homology of knot complement