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Hopf Link




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 Circle s 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 Orientation s 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

:\sigma_1^2.\,

In the Hopf Bundle

:S^1 o S^3 o S^2.\,

the fibers over any two distinct points in S^2 form a Hopf link in the 3-sphere S^3.


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