Mathematically, spin networks are related to group representation theory and can be used to construct knot invariants such as the Jones polynomial.

Partly for this reason, braided monoidal categories and various related notions are important in the theory of knot invariants.

Ribbon categories are particularly useful in constructing knot invariants.

Another more famous example is Chern-Simons theory, which can be used to compute knot invariants.

From this invariant, he defined the first of the polynomial knot invariants.

That is, we construct what mathematicians call knot invariants.

We consider wavefunctions that vanish if the loop has discontinuities and that are knot invariants.

One important context in which the Reidemeister moves appear is in defining knot invariants.

For example, many knot invariants are most easily calculated using a Seifert surface.

Many knots were shown to be hyperbolic knots, enabling the use of geometry in defining new, powerful knot invariants.