# nLab torus knot

Contents

### Context

#### Knot theory

knot theory

Examples/classes:

Types

knot invariants

Related concepts:

category: knot theory

# Contents

## 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 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.