nLab
torus knot

Idea

A torus knot is one that can be drawn on the surface of a torus. Examples include the trefoil

and cinquefoil

category: svg

knots.

Definition

A knot KK is said to be a torus knot if it can be embedded in the surface of a torus, that is, we have the map K:S 1 3K : S^1\to \mathbb{R}^3 factors through the embedding of some torus T 1S 1×S 1T_1\cong S^1\times S^1 into 2\mathbb{R}^2;

S 1KT 1embed 3S^1\stackrel{K}{\to}T_1\stackrel{embed}{\to} \mathbb{R}^3
category: knot theory

Created on December 5, 2011 at 20:01:11. See the history of this page for a list of all contributions to it.