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.
Read more about Hyperbolic Link: Examples
Famous quotes containing the word link:
“John Brown and Giuseppe Garibaldi were contemporaries not solely in the matter of time; their endeavors as liberators link their names where other likeness is absent; and the peaks of their careers were reached almost simultaneously: the Harper’s Ferry Raid occurred in 1859, the raid on Sicily in the following year. Both events, however differing in character, were equally quixotic.”
—John Cournos (1881–1956)