Thomas Fiedler

Using combinatorial tangle-valued 1-cocycles in the moduli space of long knots we define new knot invariants, which are stronger  than quantum knot invariants and poly-time calculable. Moreover, we use a 1-cocycle to define a tangle equation for each couple of knot diagrams. If the two diagrams represent the same knot, then the tangle equation has a unique solution. The tangles in this solution contain so much combinatorial information, that sometimes the knot isotopy can be recovered from them.