Hopf link
From Wikipedia, the free encyclopedia
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
- <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>.
[edit] External links
- Weisstein, Eric W., Hopf Link at MathWorld.
- The Hopf Link at the wiki Knot Atlas.
