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This is the construction / computation page for 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.

Quick Links. Ov.

<< Subfolders / Shortcuts >>  
Archive   Data   figs   nb2tex_­pdfs   OU-200716-Dror   OU-201105-Zsuzsi   OU-210101-Roland   OU-210118-Dror   /   Talks: Bangalore-2003   Projects: DPG   Talks: MoscowByWeb-2004   Talks: TrendsInLDT-2005  

<< PDF / TXT >>  
BorrBraidOUDiagram2.pdf   CinnamonRoll.pdf   CJM_Review_and_Response.pdf   main.pdf   NYJM_Reviews.pdf   OU.pdf   OUTagged.pdf   report_M_on_v1.pdf   ReverseGamma.pdf   Waterfall.pdf   /   JKTRRefereeReport.txt   recycling.txt  

<< Mathematica Notebooks >>

 Notebook (.pdf)Source (.nb)CreatedLast ModifiedSummary
1 BraidInBurauKernel source 2021-03-19 14:12:41 2021-03-19 17:41:36 Tabulating classical braids.
2 BraidsForWiest source 2020-05-17 09:14:14 2020-05-28 06:57:21 Extraction graphs for braids picked by Bert Wiest.
3 ChterentalsBraid source 2020-05-29 15:33:14 2020-05-29 16:01:19 Studying Chterental's ker(\[Psi]) virtual braid.
4 CountingClassicalBraids source 2020-05-03 16:07:53 2020-05-16 07:04:56 Counting classical braids.
5 DiamondGraphs source 2020-04-29 09:07:29 2020-05-31 09:51:28 OU matters around the Diamond Lemma.
6 DiamondMining source 2020-05-03 18:00:27 2020-05-13 18:15:35 An attempt to "mine" all the diamonds within an Extraction Graph. Fails because the notion of a diamond is not entirely well-defined, as in ExtranctionGraph[BR[3,{-1,-2,-2,-2,-1}]].
7 Diamond source 2020-04-26 19:14:25 2020-05-31 09:53:46 OU matters around the Diamond Lemma.
8 EquivalenceRelations source 2020-03-20 13:02:24 2020-03-21 15:06:04 A package to manage equivalence relations.
9 ExtractionGraphsForAllBraids source 2020-05-03 10:39:59 2020-07-06 12:53:01 All extraction graphs of all small-complexity classical braids.
10 ExtractionGraphsForKnotBraids source 2020-05-03 08:22:27 2020-05-03 08:30:56 Extraction graphs for braids representing the Rolfsen table knots.
11 ExtractionGraphsGallery source 2020-05-08 10:18:43 2020-05-16 07:04:42 A gallery of fun or noteworthy extraction graphs.
12 GraphLayouts source 2020-07-01 11:10:19 2020-07-06 12:55:37 Experiments with graph layouts.
13 index source 2020-03-08 20:23:34 2021-01-14 20:29:55 This is the index file for the 2020-03/OU project; it also produces WordCloud.png.
14 nb2tex source 2020-04-13 07:18:41 2021-02-04 19:07:25 nb2tex for the OU project.
15 OU-Programs source 2020-05-03 08:43:24 2020-06-03 10:11:04 The OU Programs (minus counting by gens and rels).
16 ReverseGamma source 2020-05-26 18:42:32 2020-07-11 12:59:10 Generating Figure fig:ReverseGamma.
17 SomeComputations source 2020-03-16 01:20:38 2021-02-04 19:06:27 The primary program accompanying "Over then Under Tangles", by Dror Bar-Natan, Zsuzsanna Dancso, and Roland van der Veen.
18 TabulatingClassicalBraids source 2020-05-29 11:41:34 2020-07-06 10:00:25 Tabulating classical braids.
19 TabulatingVirtualBraids source 2020-06-27 19:12:11 2020-06-29 08:50:51 Tabulating virtual braids.
20 TheWorstBraids source 2020-07-06 10:57:18 2020-07-06 20:03:11 Finding the braids for which the complexity of $\bar{\Gamma}$ grows in the fastest way.
21 VPBByGensAndRels source 2020-03-19 15:21:20 2020-07-06 13:24:12 Counting virtual pure braids using generators and relations. Slow and unreliable, produces only upper bounds, yet agrees with the OU computations.

<< Links >>

  1. Studied 2020-04-21 18:19:02: Diamond Lemma - MathOverflow.
  2. Studied 2020-05-11 16:34:54: Cinnamon Roll Icons - Download Free Vector Icons - Noun Project.
  3. Studied 2020-07-16 17:32:28: Dror Bar-Natan- Publications.
  4. Studied 2020-07-21 06:50:26: [2007.09828] Over then Under Tangles.
  5. Studied 2021-04-20 08:55:18: [1506.05283] Paolo Bellingeri, Bruno Aaron Cisneros de La Cruz, Luis Paris- A simple solution to the word problem for virtual braid groups.

<< Images >>

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2020-03-29.21.34.52.jpg

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2020-04-15.21.09.44.jpg

2020-04-18.15.32.12.jpg

2020-04-18.19.16.55.jpg

2020-05-26.12.09.05.jpg

20200529_200601.jpg

icon_689.png

icon.png

WordCloud.png

<< Other Files >>

abstract.old.tex   abstract.tex   arXiv.zip   a.tex   BorrBraidOUDiagram2.svg   BraidInBurauKernel.m   BraidsForWiest.m   ChterentalsBraid.m   CinnamonRoll.svg   CJM_Review_and_Response.docx   CountingClassicalBraids.m   c.tex   dbnsymb.56pk   dbnsymb.600pk   dbnsymb.mf   dbnsymb.sty   dbnsymb.tfm   defs.tex   DiamondGraphs.m   Diamond.m   DiamondMining.m   .DS_Store   EquivalenceRelations.m   ExtractionGraphsForAllBraids.m   ExtractionGraphsForKnotBraids.m   ExtractionGraphsGallery.m   f.tex   main.aux   main.brf   main.synctex.gz   main.tex   makefile   m.tex   nb2tex.m   new_aux   old_aux   OU.aux   OU.brf   OU-Programs.m   OUTagged.aux   OUTagged.brf   OU.tex   OU.zip   picins.sty   recycling.tex   refs.tex   ReverseGamma.m   SomeComputations.m   SomeComputations.tex   TabulatingClassicalBraids.m   TabulatingVirtualBraids.m   TheWorstBraids.m   tldt20.tex   t.tex   VPBByGensAndRels.m   v.tex   Waterfall.svg  


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All Files

[1506.05283] Paolo Bellingeri, Bruno Aaron Cisneros de La Cruz, Luis Paris- A simple solution to the word problem for virtual braid groups.url   [2007.09828] Over then Under Tangles.url   2020-03-29.21.34.52.jpg   2020-04-05.15.13.07.jpg   2020-04-15.21.09.44.jpg   2020-04-18.15.32.12.jpg   2020-04-18.19.16.55.jpg   2020-05-26.12.09.05.jpg   20200529_200601.jpg   abstract.old.tex   abstract.tex   arXiv.zip   a.tex   Bangalore-2003 - Shortcut.lnk   BorrBraidOUDiagram2.pdf   BorrBraidOUDiagram2.svg   BraidInBurauKernel.m   BraidInBurauKernel.nb   BraidsForWiest.m   BraidsForWiest.nb   ChterentalsBraid.m   ChterentalsBraid.nb   Cinnamon Roll Icons - Download Free Vector Icons - Noun Project.url   CinnamonRoll.pdf   CinnamonRoll.svg   CJM_Review_and_Response.docx   CJM_Review_and_Response.pdf   CountingClassicalBraids.m   CountingClassicalBraids.nb   c.tex   dbnsymb.56pk   dbnsymb.600pk   dbnsymb.mf   dbnsymb.sty   dbnsymb.tfm   defs.tex   DiamondGraphs.m   DiamondGraphs.nb   Diamond Lemma - MathOverflow.url   Diamond.m   DiamondMining.m   DiamondMining.nb   Diamond.nb   DPG - Shortcut.lnk   Dror Bar-Natan- Publications.url   .DS_Store   EquivalenceRelations.m   EquivalenceRelations.nb   ExtractionGraphsForAllBraids.m   ExtractionGraphsForAllBraids.nb   ExtractionGraphsForKnotBraids.m   ExtractionGraphsForKnotBraids.nb   ExtractionGraphsGallery.m   ExtractionGraphsGallery.nb   f.tex   GraphLayouts.nb   icon_689.png   icon.png   index.html   index.m   index.nb   JKTRRefereeReport.txt   main.aux   main.brf   main.pdf   main.synctex.gz   main.tex   makefile   MoscowByWeb-2004 - Shortcut.lnk   m.tex   nb2tex.m   nb2tex.nb   new_aux   NYJM_Reviews.pdf   old_aux   OU.aux   OU.brf   OU.pdf   OU-Programs.m   OU-Programs.nb   OUTagged.aux   OUTagged.brf   OUTagged.pdf   OU.tex   OU.zip   picins.sty   recycling.tex   recycling.txt   refs.tex   report_M_on_v1.pdf   ReverseGamma.m   ReverseGamma.nb   ReverseGamma.pdf   SomeComputations.m   SomeComputations.nb   SomeComputations.tex   TabulatingClassicalBraids.m   TabulatingClassicalBraids.nb   TabulatingVirtualBraids.m   TabulatingVirtualBraids.nb   TheWorstBraids.m   TheWorstBraids.nb   tldt20.tex   TrendsInLDT-2005 - Shortcut.lnk   t.tex   VPBByGensAndRels.m   VPBByGensAndRels.nb   v.tex   Waterfall.pdf   Waterfall.svg   WordCloud.png