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:
“This sand seemed to us the connecting link between land and water. It was a kind of water on which you could walk, and you could see the ripple-marks on its surface, produced by the winds, precisely like those at the bottom of a brook or lake. We had read that Mussulmans are permitted by the Koran to perform their ablutions in sand when they cannot get water, a necessary indulgence in Arabia, and we now understand the propriety of this provision.”
—Henry David Thoreau (1817–1862)