1-cocycles and knot invariants

We introduce an appropriate moduli space for diagrams of classical knots and we lift the Chmutov-Khoury-Rossi-Brandenbursky Gauss diagram formulas for the coefficients of the Conway polynomial to combinatorial 1-cocycles on this moduli space. In contrast to the Conway polynomial they can distinguish mirror images of knots when they are evaluated on canonical loops in the moduli space, and at least as 1-cocycles they are sensitive to the orientation of the knots.