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:
“All successful men have agreed in one thing,—they were causationists. They believed that things went not by luck, but by law; that there was not a weak or a cracked link in the chain that joins the first and last of things.”
—Ralph Waldo Emerson (1803–1882)