= Hopf link
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{wiki}
The Hopf link is the <link isotopy> class of the two coordinate <circles> in the <three-sphere>
$$
S^3=\{(z_1,z_2)\in\mathbb C^2:|z_1|^2+|z_2|^2=1\},\qquad
L=\{(e^{it},0)\}\cup\{(0,e^{it})\}.
$$
Under <stereographic projection> it has the familiar two-crossing diagram of two circles linked once. Both components are <unknots>, and their <linking number> is $+1$ or $-1$ depending on their <orientations>. Each component is a <meridian of a knot> of the other. The specific standard <link> type is part of the definition: the same component knot types and <linking number> do not in general determine a <link>.
Its <link exterior> is $T^2\times[0,1]$. Indeed, removing small neighborhoods of the two coordinate circles leaves both complex arguments free while $|z_1|$ varies in a closed interval. This product explains why exchanging the two meridians and longitudes gives the <zero surgery on the Hopf link> computation.
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