nLab torus knot

Idea

A torus knot is a knot that can be drawn on the surface of a torus.

Definition

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

$$S^1\stackrel{K}{\to}T_1\stackrel{embed}{\to} \mathbb{R}^3$$

Examples

Examples include

• the trefoil knot:

• the cinquefoil knot:

category: svg

category: knot theory