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A Very Fast, Very Strong, Topologically Meaningful and Fun Knot Invariant.
Paper PDF here: Theta.pdf. Computations here: Theta.nb.
Abstract. In this paper we introduce $\Theta=(\Delta,\theta)$, a pair of polynomial knot invariants which is:
- Theoretically and practically fast: $\Theta$ can be computed in polynomial time and we computed it in full on random knots with over 300 crossings, and its evaluation on on simple rational numbers on random knots with over 700 crossings.
- Strong: Its separation power is much greater than, say, the HOMFLY-PT polynomial and Khovanov homology (taken together) on knots with up to 15 crossings (while computing much faster).
- Topologically meaningful: It gives a genus bound, and there are reasons to hope that it would do more.
- Fun: Scroll to Figures 1.1, 1.2, and 3.1.
<< Mathematica Notebooks >>
| Notebook (.pdf) | Source (.nb) | Created | Last Modified | Summary | |
|---|---|---|---|---|---|
| 1 | index | source | Tue 10 Sep 2024 12:37:57 | Sun 2 Feb 2025 10:40:59 | This is the index file for the Theta project. |
| 2 | Make | source | Sun 17 Nov 2024 11:56:59 | Sat 11 Jan 2025 16:30:02 | |
| 3 | Theta@241230 | source | Mon 30 Dec 2024 12:45:15 | Mon 30 Dec 2024 12:15:55 | This is the main Mathematica package that goes along with the paper "A Very Fast, Very Strong, Topologically Meaningful and Fun Knot Invariant" by Dror Bar-Natan and Roland van der Veen. |
| 4 | Theta-Antisymmetric | source | Fri 6 Dec 2024 22:32:12 | Fri 6 Dec 2024 22:54:43 | |
| 5 | Theta | source | Mon 16 Sep 2024 10:34:48 | Fri 24 Jan 2025 11:48:01 | This is the main Mathematica package that goes along with the paper "A Very Fast, Very Strong, Topologically Meaningful and Fun Knot Invariant" by Dror Bar-Natan and Roland van der Veen. |
<< Links >>
- Studied Fri 20 Dec 2024 14:10:08: The two-loop knot invariant Theta.
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