nLab
link invariant

Link invariants

Idea

Many of the knot invariants have analogues for links. Some, in fact seem to be better thought of as being restrictions of link invariants to single component links (i.e. knots). We repeat the statement from knot invariant with obvious adjustments.

Definition

A link invariant is map from isotopy classes of links to any kind of structure you could imagine. These are helpful because it’s much easier to check that the structures one maps to (numbers, groups, etc.) are different than it is to check that links are different.

Examples

Revised on October 5, 2010 11:16:09 by Toby Bartels (98.16.135.82)