Types of knot invariants

Question

Knot invariants seem to roughly be either numbers (that is, an amount of something ), polynomials, matrices, or groups. Are there any other invariants that have been studied that are not of this form?

Thank you

Answer 1

Sure. For example,

• Khovanov homology is a bigraded abelian group,
• the knot quandle is a quandle,
• the Kontsevich integral is an element of the algebra of chord diagrams.