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:
“This sand seemed to us the connecting link between land and water. It was a kind of water on which you could walk, and you could see the ripple-marks on its surface, produced by the winds, precisely like those at the bottom of a brook or lake. We had read that Mussulmans are permitted by the Koran to perform their ablutions in sand when they cannot get water, a necessary indulgence in Arabia, and we now understand the propriety of this provision.”
—Henry David Thoreau (1817–1862)