::Torus knot
::concepts
A (3,−7)-3D torus knot.
EureleA Award showing a (2,3)-torus knot.
(2,8) torus link
-Torus_Link.svg)
{{#invoke:Hatnote|hatnote}} In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of coprime integers p and q. A torus link arises if p and q are not coprime (in which case the number of components is gcd(p, q)). A torus knot is trivial (equivalent to the unknot) if and only if either p or q is equal to 1 or −1. The simplest nontrivial example is the (2,3)-torus knot, also known as the trefoil knot.
Torus knot sections
Intro Geometrical representation Properties Connection to complex hypersurfaces List See also References External links
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{{#invoke:Hatnote|hatnote}} In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of coprime integers p and q. A torus link arises if p and q are not coprime (in which case the number of components is gcd(p, q)). A torus knot is trivial (equivalent to the unknot) if and only if either p or q is equal to 1 or −1. The simplest nontrivial example is the (2,3)-torus knot, also known as the trefoil knot.
Torus knot sections
Intro Geometrical representation Properties Connection to complex hypersurfaces List See also References External links
| PREVIOUS: Intro | NEXT: Geometrical representation |
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