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Abstract. Following Rozansky [Ro1, Ro2, Ro3] and Overbay [Ov], we construct the first poly-time-computable knot polynomials since Alexander's [Al, 1928]. We use some new commutator-calculus techniques and a family of Lie algebra $sl_2^{\leq k}$ which are solvable yet at the same time they make progressively better approximations of the simple Lie algebra $sl_2$. The resulting invariants are the strongest genuinely-computable knot invariants presently available and they seem to contain information about some classical topologically-defined knot invariants.
Quick Links. Ov.
Archive figs PPSA-170103 Snips VSnips / People: VanDerVeen CS-PPSA.pdf PPSA.pdf PPSATagged.pdf / recycling.txt<< Notebook Pages >>
| Page | Created (UT) | Last Modified (UT) | |
|---|---|---|---|
| 1 | Planning 170624 | 2017-06-24 14:21:50 | 2017-06-24 16:03:41 |
<< Mathematica Notebooks >>
| Notebook (.pdf) | Source (.nb) | Created | Last Modified | Summary | |
|---|---|---|---|---|---|
| 1 | CellExport | source | 2017-07-06 10:09:00 | 2017-12-19 15:59:49 | A program for exporting tagged cells, continues pensieve://Projects/WKO4/. |
| 2 | index | source | 2016-09-17 11:43:49 | 2017-12-19 15:22:20 | This is the index file for the PPSA project. |
| 3 | MakeSnips | source | 2017-12-19 14:58:01 | 2017-12-19 16:24:07 | Make the snip files in Snips/. |
| 4 | MakeVSnips | source | 2017-12-19 16:23:13 | 2018-02-11 08:43:20 | Make the snip files in VSnips/. |
| 5 | ReorderingDemo-170704 | source | 2017-07-04 12:59:31 | 2017-07-05 11:00:09 | |
| 6 | ReorderingDemo | source | 2017-07-05 10:24:38 | 2017-12-19 15:18:46 | Reordering exponentials in $sl_2$ and in ${\mathfrak g}_0$. |
| 7 | Verification | source | 2018-02-10 12:55:53 | 2018-02-11 12:03:27 | A unified verification notebook for the PPSA project; continued pensieve://Projects/SL2Portfolio/. |
<< Links >>
- Studied 2017-06-28 14:44:15: [1004.1214v1] Kauffman, Radford- Oriented Quantum Algebras and Coalgebras, Invariants of Oriented 1-1 Tangles, Knots and Links.
- Studied 2017-06-28 14:44:44: [math0505219] Habiro- Bottom tangles and universal invariants.
- Studied 2017-12-18 08:35:15: Automatically execute command after save - Mathematica Stack Exchange.
<< Images >>
