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… … Wikipedia
Knot invariant — In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence is often given by ambient isotopy but can be given by homeomorphism. Some… … Wikipedia
List of knot theory topics — Knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician s knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical… … Wikipedia
Knot theory — A three dimensional depiction of a thickened trefoil knot, the simplest non trivial knot … Wikipedia
Hyperbolic 3-manifold — A hyperbolic 3 manifold is a 3 manifold equipped with a complete Riemannian metric of constant sectional curvature 1. In other words, it is the quotient of three dimensional hyperbolic space by a subgroup of hyperbolic isometries acting freely… … Wikipedia
Hyperbolic group — In group theory, a hyperbolic group, also known as a word hyperbolic group, Gromov hyperbolic group, negatively curved group is a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic… … Wikipedia
Alternating knot — In knot theory, a link diagram is alternating if the crossings alternate under, over, under, over, as you travel along each component of the link. A link is alternating if it has an alternating diagram.Many of the knots with crossing number less… … Wikipedia
Mutation (knot theory) — The Kinoshita–Terasaka knot and the Conway knot respectively, and how they are related by mutation. In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the… … Wikipedia
Figure-eight knot (mathematics) — In knot theory, a figure eight knot (also called Listing s knot) is the unique knot with a crossing number of four. This is the smallest possible crossing number except for the unknot and trefoil knot. Origin of name The name is given because… … Wikipedia
6₂ knot — The 62 knot. In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot. This knot is sometimes referred to as the Miller Institute knot[1], because is appea … Wikipedia
