hopf link

In mathematical knot theory, the Hopf link 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

\sigma_1^2

In the Hopf bundle

S^1 \to S^3 \to 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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