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:
“To one who is accustomed to thinking a lot, every new thought that he hears or reads about immediately appears as a link in a chain.”
—Friedrich Nietzsche (1844–1900)