Hopf link

In mathematical knot theory, the Hopf link 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

<math>\sigma_1^2<math>.

In the Hopf bundle

<math>S^1 \to S^3 \to S^2<math>

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

External links

• Eric W. Weisstein, Hopf Link at MathWorld.