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 makeT 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.
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Penne, R. Yang-Baxter invariants for line configurations. Discrete Comput Geom 15, 15–33 (1996). https://doi.org/10.1007/BF02716577
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DOI: https://doi.org/10.1007/BF02716577