nLab
knot invariant

Contents

Idea

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

Examples

Many of these extend to link invariants or have variants that depend on the knot being oriented.

References

Discussion of knot invariants in terms of BPS states in string theory includes

category: knot theory

Revised on June 11, 2015 17:31:00 by Urs Schreiber (62.48.248.82)