This webpage contains various interactive plots and comparison tools that supplement the papers [arXiv; GitHub] and [arXiv; GitHub]. Relevant knot invariant data, scripts and more details on data collection are available on the corresponding GitHub pages. Most data displayed on this webpage considers all prime knots (not distinguishing mirrors) up to 16 crossings. More computable invariants have data up to 19 crossings, while harder invariants have lower values.
Notice! While the website probably works on phones, less care has been put into polishing the mobile experience.
Warning! The Ballmapper page and old versions of the website fetch large files (~30-50MB per figure). So beware if you have bandwidth limits or slow internet.
The analogous webpage for Kazhdan--Lusztig polnomials can be found here.
Short descriptions of the invariants and their abbreviations used in some plots.
| Name | Abbreivation | Description |
|---|---|---|
| A2 | A2 | SL3 polynomial |
| Alexander | A | Alexander polynomial |
| B1 | B1 | SO3 Polynonmial; 2 coloured Jones polynomial |
| BV | BV | Bar-Natan and van der Veen's Theta (non Alexander part) |
| BVSp | BVSp | Bar-Natan and van der Veen's Theta (non Alexander part) specialised at t1=22/7, t2=21/13 |
| Alexander+BV | A+BV | Bar-Natan and van der Veen's Theta (full) |
| AlexanderSp+BVSp | ASp+BVSp | Bar-Natan and van der Veen's Theta (full) specialised at t1=22/7, t2=21/13 |
| HFK2 | HFK2 | HFK homology (p=2) |
| HFK2T1 | HFK2T1 | HFK homology (p=2) specialising t=1 |
| HOMFLYPT | H | HOMFLYPT polynomial |
| HOMFLYPTHomology | HH | HOMFLYPT homology |
| Jones | J | Jones polynomial |
| Khovanov | K | Khovanov homology |
| KhovanovT1 | KT1 | Khovanov homology specialising t=1 |
| KhovanovOdd | KO | Odd Khovanov homology |
| KR3 | KR3 | SL3 homology (Khovanov--Rozansky) |
| V1 | V1 | Nichols algebra version of the Links-Gould polynomial |
| V2 | V2 | Higher version of V1 |
| All | All | Everything together |
| J+KT1 | J+KT1 | Jones and KhovanovT1 together |