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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 | 2024-09-10 12:37:57 | 2024-11-12 12:09:51 | This is the index file for the Theta project. |
| 2 | Make | source | 2024-11-17 11:56:59 | 2024-12-15 09:46:27 | |
| 3 | Theta-Antisymmetric | source | 2024-12-06 22:32:12 | 2024-12-06 22:54:43 | |
| 4 | Theta | source | 2024-09-16 10:34:48 | 2024-12-15 10:43:49 | 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. |
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