The tangle-valued 1-cocycle for knots

We replace the Yang-Baxter equation by the tetrahedron equation and use it to construct an infinit ordered set of Alexander (or Conway) polynomials, called the Alexander tree, as a knot invariant. As an application we prove that the knot 8_17 is not invertible by using just the first coefficients of some of the Conway polynomials in the invariant. This makes the Alexander tree a serious candidate for a complete and calculable invariant for classical knots.