In mathematical knot theory, the Hopf link, named after Heinz Hopf, is the simplest nontrivial link with more than one component. It consists of two circles linked together exactly once. For a concrete model take the unit circle in the xy-plane centered at the origin and another unit circle in the yz-plane centered at (0,1,0).

Depending on the relative orientations of the two components the linking number of the Hopf link is ±1.

The Hopf link is a (2,2)-torus link with the braid word

$\backslash sigma\_1^2.\backslash ,$

In the Hopf bundle

$S^1\; \backslash to\; S^3\; \backslash to\; S^2.\backslash ,$

the fibers over any two distinct points in $S^2$ form a Hopf link in the 3-sphere $S^3$.

External links

• The Hopf Link at the wiki Knot Atlas.

Knot theory | Eponyms