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
In the Hopf bundle
The fibers over any two distinct points in S2 form a Hopf link in the 3-sphere S3.
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Famous quotes containing the word link:
“We fight our way through the massed and leveled collective safe taste of the Top 40, just looking for a little something we can call our own. But when we find it and jam the radio to hear it again it isn’t just ours—it is a link to thousands of others who are sharing it with us. As a matter of a single song this might mean very little; as culture, as a way of life, you can’t beat it.”
—Greil Marcus (b. 1945)