Rosso-Jones formula for colored HOMFLY of torus knots
and matrix model representations (HOMFLY as averages of characters)
Papers:
- M.Rosso and V.F.R.Jones, J. Knot Theory Ramifications, $\textbf{2}$ (1993) 97-112;
- X.-S.Lin and H.Zheng, Trans. Amer. Math. Soc. $\textbf{362}$ (2010) 1-18, math/0601267;
- A.Brini, B.Eynard and M.Marino, Annales Henri Poincare. Vol. 13. No. 8. SP Birkhauser Verlag Basel, 2012, arXiv:1105.2012;
- A.Alexandrov, A.Mironov, A.Morozov and An.Morozov, JETP Letters ${\bf 100}$ (2014) 271-278 (Pis'ma v ZhETF ${\bf 100}$ (2014) 297-304), arXiv:1407.3754;
- A.Alexandrov, D.Melnikov, Matrix integral expansion of colored Jones polynomials for figure-eight knot. JETP Letters, ${\bf 101}$, (2015) 51-56, arXiv:1411.5698;
- P.Ramadevi and T.Sarkar, On Link Invariants and Topological String Amplitudes, Nucl.Phys. ${\bf B600}$ (2001) 487-511, hep-th/0009188;
- A.Mironov, A.Morozov and A.Sleptsov, JHEP ${\bf 07}$ (2015) 069, arXiv:1412.8432
Colored HOMFLY vs AMM/EO topological recursion:
- R.Dijkgraaf, H.Fuji and M.Manabe, The volume conjecture, perturbative knot invariants, and recursion relations for topological strings, Nuclear Physics B ${\bf 849}$, (2011), 166-211, arxiv:1010.4542;
- S. Gukov, P. Sulkowski, A-polynomial, B-model, and Quantization, JHEP 1202 (2012) 070, arXiv:1108.0002;
- J.Gu, H.Jockers, A.Klemm, M.Soroush, Knot Invariants from Topological Recursion on Augmentation Varieties, Comm.Math.Phys. $\bf{ 336.2}$ (2014), 987-1051, arXiv:1401.5095