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Abstract. Over-then-Under (OU) tangles are oriented tangles whose strands travel through all of their over crossings before any under crossings. In this paper we discuss the idea of gliding: an algorithm by which tangle diagrams could be brought to OU form. By analyzing cases in which the algorithm converges, we obtain a braid classification result, which we also extend to virtual braids, and provide a Mathematica implementation. We discuss other instances of successful "gliding ideas" in the literature - sometimes in disguise - such as the Drinfel'd double construction, Enriquez's work on quantization of Lie bialgebras, and Audoux and Meilhan's classification of welded homotopy links.
figs nb2tex_pdfs BorrBraidOUDiagram2.pdf CinnamonRoll.pdf OU.pdf ReverseGamma.pdf Waterfall.pdf<< Mathematica Notebooks >>
| Notebook (.pdf) | Source (.nb) | Created | Last Modified | Summary | |
|---|---|---|---|---|---|
| 1 | index | source | 2024-03-17 11:29:03 | 2022-11-10 13:54:09 | This is the index file for the 2020-03/OU/OU-221110-JKTR project. |
| 2 | nb2tex | source | 2024-03-17 11:29:03 | 2022-11-10 12:28:30 | nb2tex for the OU project. |
| 3 | SomeComputations | source | 2024-03-17 11:29:03 | 2022-11-10 14:06:39 | The primary program accompanying "Over then Under Tangles", by Dror Bar-Natan, Zsuzsanna Dancso, and Roland van der Veen. |
