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This is the construction / computation page for the JKTR version of my joint paper with Zsuzsanna Dancso and Roland van der Veen, Over then Under Tangles (PDF here, data files here).

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.

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figs   nb2tex_­pdfs  

<< PDF >>  
BorrBraidOUDiagram2.pdf   CinnamonRoll.pdf   OU.pdf   ReverseGamma.pdf   Waterfall.pdf  

<< Mathematica Notebooks >>

 Notebook (.pdf)Source (.nb)CreatedLast ModifiedSummary
1 index source 2022-11-10 12:43:59 2022-11-10 12:54:09 This is the index file for the 2020-03/OU/OU-221110-JKTR project.
2 nb2tex source 2022-11-10 11:05:23 2022-11-10 11:28:30 nb2tex for the OU project.
3 SomeComputations source 2022-11-10 11:03:35 2022-11-10 13:06:39 The primary program accompanying "Over then Under Tangles", by Dror Bar-Natan, Zsuzsanna Dancso, and Roland van der Veen.

<< Other Files >>

abstract.tex   a.tex   BorrBraidOUDiagram2.svg   CinnamonRoll.svg   c.tex   dbnsymb.47pk   dbnsymb.56pk   dbnsymb.600pk   dbnsymb.mf   dbnsymb.sty   dbnsymb.tfm   defs.tex   enumitem.sty   f.tex   jktr-2e.zip   main.tex   makefile   m.tex   nb2tex.m   new_aux   old_aux   OU.aux   OU.brf   OU.tex   OU.zip   picins.sty   refs.tex   SomeComputations.m   SomeComputations.tex   tldt20.tex   t.tex   v.tex   Waterfall.svg   ws-jktr.cls  


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figs   nb   nb2tex_pdfs  

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abstract.tex   a.tex   BorrBraidOUDiagram2.pdf   BorrBraidOUDiagram2.svg   CinnamonRoll.pdf   CinnamonRoll.svg   c.tex   dbnsymb.47pk   dbnsymb.56pk   dbnsymb.600pk   dbnsymb.mf   dbnsymb.sty   dbnsymb.tfm   defs.tex   enumitem.sty   f.tex   index.html   index.m   index.nb   jktr-2e.zip   main.tex   makefile   m.tex   nb2tex.m   nb2tex.nb   new_aux   old_aux   OU.aux   OU.brf   OU.pdf   OU.tex   OU.zip   picins.sty   refs.tex   ReverseGamma.pdf   SomeComputations.m   SomeComputations.nb   SomeComputations.tex   tldt20.tex   t.tex   v.tex   Waterfall.pdf   Waterfall.svg   ws-jktr.cls