Yang-Baxter invariants for line configurations |
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Authors: | R Penne |
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Institution: | (1) Department of Mathematics and Computer Science, University of Antwerp (UIA), Wilrijk, Antwerp, Belgium |
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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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Keywords: | |
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