Yang-Baxter invariants for line configurations
Faculty of Sciences. Mathematics and Computer Science
New York, N.Y.
Discrete and computational geometry. - New York, N.Y.
, p. 15-33
University of Antwerp
We study line configurations in 3-space by means of ''line diagrams,'' projections into a plane with an indication of over and under crossing at the vertices. If we orient such a diagram, we can associate a ''contracted tensor'' T with it in the same spirit as is done in Knot Theory. We give conditions to make T independent of the orientation, and invariant under isotopy. The Yang-Baxter equation is one such condition. Afterwards we restrict ourselves to Yang-Baxter invariants with a topological state model, and give some new invariants for line isotopy.