## ::Torus knot

### ::concepts

{{#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 **R**^{3}. 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 |

<< | >> |

{{#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 **R**^{3}. 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 |

<< | >> |