Timeline for Proving that the Jones polynomial is q-holonomic
Current License: CC BY-SA 3.0
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| Sep 12, 2014 at 21:38 | comment | added | Peter Samuelson | I'll update this answer if I figure out this proof, it's an interesting question. There's another heuristic reason why the Jones polys are holonomic, although again I'm not sure if it can be turned into a proof. When $q=1$, the skein module of a 3-manifold $M$ is the ring of functions of the scheme $Char(M) := Hom(\pi_1(M), SL_2(\mathbb {C})) / SL_2(\mathbb{C})$ (the character variety). If $M$ is a knot complement, it is known that the image of the restriction map $Char(M) \to Char(\partial M)$ is Lagrangian. One might then expect that its quantization (the skein module) should be holonomic. | |
| Sep 10, 2014 at 4:30 | comment | added | Gjergji Zaimi | Thanks, this was very helpful! I would be curious to see a proof of holonomicity using the cabling formula involving the polynomial representation of DAHA. I will check the references you gave. | |
| Sep 9, 2014 at 4:19 | history | answered | Peter Samuelson | CC BY-SA 3.0 |