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

knots.

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 3 factors through the embedding of some torus T 1S 1×S 1 into 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 20:19:45 by Tim Porter (95.147.237.179)