framed link


A framed link is a link where the circles forming the components are viewed as having a thickness, albeit an arbitrarily small thickness. That is to say, instead of the components of the links being embedded circles, they are embedded solid tori.

The thickening can be considered in one direction only which gives embedded ribbons. This is an equivalent definition which can be useful as it makes the distinction clearer between an embedding and the same embedding composed with, say, a Dehn twist.

A link diagram can be made into a diagram of a framed links by giving it the blackboard framing: this views each segment of the link diagram as a ribbon lying on the “blackboard”.

Two diagrams represent the same link diagram if and only if they can be related by a modified version of the Reidemeister moves in which the first move is replaced by the following move.

Revised on March 31, 2011 13:27:17 by Andrew Stacey (