nLab
torus knot

Contents

Contents

Idea

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

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 3\mathbb{R}^3;

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

Examples

Examples include

  • the cinquefoil knot:
category: svg
category: knot theory

Last revised on January 26, 2021 at 01:48:45. See the history of this page for a list of all contributions to it.