YANG-BAXTER INVARIANTS FOR LINE CONFIGURATIONS

We study line configurations in 3-space by means of ''line diagrams,'' projections into a plane with an indication of over and under crossin g at the vertices. If we orient such a diagram, we can associate a ''c ontracted tensor'' T with it in the same spirit as is done in Knot The ory. We give conditions to make T independent of the orientation, and invariant under isotopy. The Yang-Baxter equation is one such conditio n. Afterwards we restrict ourselves to Yang-Baxter invariants with a t opological state model, and give some new invariants for line isotopy.