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Hyperbolic link : ウィキペディア英語版 | Hyperbolic link
In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry. A hyperbolic knot is a hyperbolic link with one component. As a consequence of the work of William Thurston, it is known that every knot is precisely one of the following: hyperbolic, a torus knot, or a satellite knot. As a consequence, hyperbolic knots can be considered plentiful. A similar heuristic applies to hyperbolic links. As a consequence of Thurston's hyperbolic Dehn surgery theorem, performing Dehn surgeries on a hyperbolic link enables one to obtain many more hyperbolic 3-manifolds. ==Examples==
*Borromean rings are hyperbolic. *Every non-split, prime, alternating link that is not a torus link is hyperbolic by a result of William Menasco. *4₁ knot *5₂ knot *6₁ knot *6₂ knot *6₃ knot *7₄ knot *10 161 knot *12n242 knot
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