Two complete invariants of oriented knots
arXiv:2306.00954
Abstract
We construct two complete invariants of oriented classical knots in space. The value of each invariant on any knot is a set, infinite for the first invariant and finite for the second. The finite set is computed algorithmically from any knot diagram in a finite number of steps. The algorithm reveals the knotting number of the knot as well.
104 pages, 51 figures