Yang-Baxter invariants for line configurations

Abstract

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.

Spindle-configurations of skew lines

“…The study and classification of configurations of skew lines (up to isotopy) was started by Viro [19] and continued for example in [1], [2], [3], [6], [10], [13], [14], [15], [16] and [20].…”