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This is the construction / computation page for my paper Finite Type Invariants of w-Knotted Objects IV: Some Computations (PDF here).

Click to download the main Mathematica packages used within: FreeLie.m and AwCalculus.m.

Abstract. In the previous three papers in this series, [WKO1]-[WKO3], Z. Dancso and I studied a certain theory of "homomorphic expansions" of "w-knotted objects", a certain class of knotted objects in 4-dimensional space. When all layers of interpretation are stripped off, what remains is a study of a certain number of equations written in a family of spaces ${\mathcal A}^w$, closely related to degree-completed free Lie algebras and to degree-completed spaces of cyclic words.

The purpose of this paper is to introduce mathematical and computational tools that enable explicit computations (up to a certain degree) in these ${\mathcal A}^w$ spaces and to use these tools to solve the said equations and verify some properties of their solutions, and as a consequence, to carry out the computation (up to a certain degree) of certain knot-theoretic invariants discussed in [WKO1]-[WKO3] and in my related paper [KBH].

Front page links: WKO4.pdf, FreeLie.m, AwCalculus.m, WKO4Session (nb, pdf), bch (nb, pdf), 817 (nb, pdf), Borromean (nb, pdf), VCapSolution (nb, pdf), KVDirect (nb, pdf), dims (nb, pdf), dims1 (nb, pdf), Phi (nb, pdf).

<< Subfolders / Shortcuts >>  
Archive   ComputerTalk   figs   /   2013-04   2014-01   2013-11: DoubleTree  

<< PDF / TXT >>  
CheatSheetFreeLie.pdf   WKO4.pdf   WKO4Tagged.pdf   /   abstract.txt   listing.txt   recycling.txt  

<< Notebook Pages >>

 PageCreated (UT)Last Modified (UT)
1 Goals 2014-02-28 22:04:37 2014-02-28 22:10:27
2 $\Gamma$, $\Lambda$ 2014-03-13 15:41:49 2014-03-19 18:38:12
3 Proof of the Conversion Theorem 2014-06-25 18:57:23 2015-10-05 23:42:04
4 --- Comparing Products 2014-08-06 00:53:54 2014-08-06 14:03:26
5 --- In Pictures 2014-08-07 11:05:36 2014-08-07 11:24:30
6 --- Why Same? 2014-09-02 13:25:47 2014-09-02 13:29:45
(.one source file for all pages above)

<< Mathematica Notebooks >>

 Notebook (.pdf)Source (.nb)CreatedLast ModifiedSummary
1 817 source 2015-12-17 20:19:02 2015-12-20 11:45:34 Fuller output of for $8_{17}$.
2 AwCalculus source 2015-12-17 20:19:02 2015-09-10 19:21:15 Aw-calculus programs for the WKO4 paper.
3 AwCalculus-Testing source 2015-12-17 20:19:02 2015-02-12 12:50:58 Testing the AwCalculus package.
4 bch source 2015-12-17 20:19:02 2015-12-21 14:54:52 Fuller output of bch. Even fuller: bch-to-20.m, bch-to-22.m, bch-to-23.m.
5 bch-stats source 2016-01-11 11:37:23 2016-01-11 13:54:07 Fuller output of bch. Even fuller: bch-to-20.m, bch-to-22.m, bch-to-23.m.
6 Borromean source 2015-12-17 20:19:02 2015-12-21 19:20:02 Fuller output of for the Borromean tangle. Even fuller: Borromean-to-7.m
7 CellExport source 2015-12-17 20:19:02 2017-07-06 10:10:02 A program for exporting tagged cells, continues pensieve://2013-03/, continued pensieve://Projects/PPSA/.
8 CheatSheetFreeLie-Verification source 2015-12-17 20:19:02 2014-09-09 15:14:12 Cheat Sheet Free Lie Verification; continues CheatSheetJ-Verification @ pensieve://2014-01/.
9 Debugging-150909 source 2015-12-17 20:19:03 2015-09-09 20:59:10  
10 dims1 source 2015-12-17 20:19:03 2015-05-31 04:17:10 The linearized KV and twist equations.
11 dims2 source 2015-12-17 20:19:03 2015-05-29 16:20:45 The linearized tree-level KV and twist equations.
12 dims3 source 2015-12-17 20:19:03 2015-05-29 16:19:56 The linearized tree-level KV equations.
13 dims source 2015-12-17 20:19:03 2015-05-29 06:38:42 The linearized KV equations.
14 FlipSymmetry source 2015-12-17 20:19:03 2015-04-27 08:35:18 Testing if vertical flip is a symmetry of SolKV.
15 FollowingAlbertHarinckTorossian source 2015-12-17 20:19:03 2015-05-28 11:47:04 Calculations following Albert-Harinck-Torossian's arXiv:0802.2049.
16 FreeLie source 2015-12-17 20:19:03 2015-11-05 19:19:59 A free-Lie calculator, pensieve://Projects/WKO4/ branch (most current), continues pensieve://2014-01/. Now understands the Drinfel'd-Kohno algebra.
17 FreeLie-Testing source 2015-12-17 20:19:03 2015-04-21 21:06:39 Testing the FreeLie package.
18 index source 2015-12-17 20:19:03 2016-02-05 10:36:10  
19 KVDirect source 2015-12-17 20:19:03 2015-08-07 16:35:24 Fuller output of for the direct KV solution. Even fuller: KVDirect-to-13.m.
20 Make source 2015-12-17 20:19:03 2016-07-25 19:57:47  
21 muCalculus source 2015-12-17 20:19:03 2014-02-24 15:45:36 μ-calculus programs, continues pensieve://2013-11/DoubleTree/.
22 Phi source 2015-12-17 20:19:03 2015-04-17 07:43:14 Fuller output of for a Drinfel'd associator Φ.
23 Recycling source 2015-12-17 20:19:03 2015-02-05 19:33:20  
24 Trialities source 2015-12-17 20:19:03 2015-08-05 20:55:00 Figuring out triality(s).
25 VCapFlipSolution source 2015-12-17 20:19:04 2015-05-04 09:09:24 Solving R4, Unitarity, Cap, and Vertical Flip. Data file: R4UniCapVFlipSolution-to-12.m.
26 VCapSolution source 2015-12-17 20:19:04 2015-11-18 19:59:16 Fuller output of for V and Cap. Even fuller: VCapSolution-to-12.m.
27 VCapTwistSolution source 2015-12-17 20:19:04 2015-04-19 10:39:14 Solving R4, Unitarity, Cap, and Twist.
28 WKO4Session source 2015-12-17 20:19:04 2016-07-25 19:55:18 Calculations appearing in the WKO4 paper.

<< Links >>

  1. Studied 2014-03-26 13:50:02: CTAN Package bigfoot.
  2. Studied 2015-02-11 10:16:06: Int. J. of Alg. & Computation.
  3. Studied 2015-11-18 22:33:45: [1511.05624] Finite Type Invariants of w-Knotted Objects IV Some Computations.
  4. Studied 2017-05-04 16:15:18: Journal of Applied and Computational Topology.

<< Images >>


GammaAndLambda-140826.jpg

Icon_120.png

Logo.png

NotationRewrite-141022.jpg

TempLogo.png

WordCloud.png

<< Other Files >>

817.m   abstract.sed   abstract.tex   arXiv.zip   AwCalculus.m   AwCalculus-Testing.m   bch.m   bch-to-20.m   bch-to-22.m   bch-to-23.m   Borromean.m   Borromean-to-7.m   CellExport.m   CheatSheetFreeLie.aux   CheatSheetFreeLie.synctex   CheatSheetFreeLie.tex   CheatSheetFreeLie-Verification.m   comp.tex   dbnsymb.39pk   dbnsymb.51pk   dbnsymb.56pk   dbnsymb.600pk   dbnsymb.mf   dbnsymb.sty   dbnsymb.tfm   defs.tex   El.tex   FlipSymmetry.m   FollowingAlbertHarinckTorossian.m   FreeLie.m   FreeLie-Testing.m   glossary.tex   intro.tex   KBH.aux   KVDirect.m   KVDirect-to-13.m   macros.tex   main.tex   makefile   Make.m   muCalculus.m   new_aux   old_aux   Phi.m   picins.sty   R4UniCapVFlipSolution-to-12.m   Recycling.nb.tex   recycling.tex   refs.tex   ToDo.tex   Trialities.m   VCapFlipSolution.m   VCapSolution.m   VCapSolution-to-11.m   VCapSolution-to-12.m   VCapTwistSolution.m   WKO1.aux   WKO2.aux   WKO4.aux   WKO4.brf   WKO4.m   WKO4Session.m   WKO4Tagged.aux   WKO4Tagged.brf   WKO4.tex  


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[1511.05624] Finite Type Invariants of w-Knotted Objects IV Some Computations.URL   2013-04 - Shortcut.lnk   2014-01 - Shortcut.lnk   817.m   817.nb   abstract.sed   abstract.tex   abstract.txt   arXiv.zip   AwCalculus.m   AwCalculus.nb   AwCalculus-Testing.m   AwCalculus-Testing.nb   bch.m   bch.nb   bch-stats.nb   bch-to-20.m   bch-to-22.m   bch-to-23.m   Borromean.m   Borromean.nb   Borromean-to-7.m   CellExport.m   CellExport.nb   CheatSheetFreeLie.aux   CheatSheetFreeLie.pdf   CheatSheetFreeLie.synctex   CheatSheetFreeLie.tex   CheatSheetFreeLie-Verification.m   CheatSheetFreeLie-Verification.nb   comp.tex   CTAN Package bigfoot.URL   dbnsymb.39pk   dbnsymb.51pk   dbnsymb.56pk   dbnsymb.600pk   dbnsymb.mf   dbnsymb.sty   dbnsymb.tfm   Debugging-150909.nb   defs.tex   dims1.nb   dims2.nb   dims3.nb   dims.nb   DoubleTree - Shortcut.lnk   El.tex   FlipSymmetry.m   FlipSymmetry.nb   FollowingAlbertHarinckTorossian.m   FollowingAlbertHarinckTorossian.nb   FreeLie.m   FreeLie.nb   FreeLie-Testing.m   FreeLie-Testing.nb   GammaAndLambda-140826.jpg   glossary.tex   Icon_120.png   index.html   index.m   index.nb   Int. J. of Alg. & Computation.URL   intro.tex   Journal of Applied and Computational Topology.URL   KBH.aux   KVDirect.m   KVDirect.nb   KVDirect-to-13.m   listing.txt   Logo.png   macros.tex   main.tex   makefile   Make.m   Make.nb   muCalculus.m   muCalculus.nb   new_aux   NotationRewrite-141022.jpg   old_aux   Phi.m   Phi.nb   picins.sty   R4UniCapVFlipSolution-to-12.m   Recycling.nb   Recycling.nb.tex   recycling.tex   recycling.txt   refs.tex   TempLogo.png   ToDo.tex   Trialities.m   Trialities.nb   VCapFlipSolution.m   VCapFlipSolution.nb   VCapSolution.m   VCapSolution.nb   VCapSolution-to-11.m   VCapSolution-to-12.m   VCapTwistSolution.m   VCapTwistSolution.nb   WKO1.aux   WKO2.aux   WKO4.aux   WKO4.brf   WKO4.m   WKO4.pdf   WKO4Session.m   WKO4Session.nb   WKO4Tagged.aux   WKO4Tagged.brf   WKO4Tagged.pdf   WKO4.tex   WordCloud.png