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We discuss two realizations of the colored Jones polynomials of a knot, one from an unnoticed work of the second author in 1994 on quantum R-matrices at roots of unity obtained from solutions of the pentagon identity, and another one from recent work of D.
Rinat Kashaev, Invariants of long knots , Preprint 2019, arXiv:1908.00118
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by same author, Quantum dilogarithm as a 6 j 6j -symbol , Modern Phys. Lett. A 9
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Thang T. Q. Lê, The colored Jones polynomial and the A A -polynomial of knots , Adv. Math. 207
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Jim Hoste and Patrick Shanahan, Trace fields of twist knots , J. Knot Theory Ramifications 10
2001
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Hitoshi Murakami and Jun Murakami, The colored Jones polynomials and the simplicial volume of a knot , Acta Math. 186
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Kazuo Habiro, On the quantum sl 2 \rm sl_{2} invariants of knots and integral homology spheres , Invariants of knots and 3-manifolds (Kyoto, 2001), Geom. Topol. Monogr., vol. 4, Geom. Topol. Publ., Coventry, 2002, pp. 55–68 (electronic)
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Gregor Masbaum, Skein-theoretical derivation of some formulas of Habiro , Algebr. Geom. Topol. 3
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Stavros Garoufalidis, On the characteristic and deformation varieties of a knot , Proceedings of the Casson Fest, Geom. Topol. Monogr., vol. 7, Geom. Topol. Publ., Coventry, 2004, pp. 291–309
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by same author, Cyclotomic completions of polynomial rings , Publ. Res. Inst. Math. Sci. 40
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by same author, HolonomicFunctions (user’s guide) , Tech. Report 10-01, RISC Report Series, Johannes Kepler University Linz, 2010
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Don Zagier, Quantum modular forms , Quanta of maths, Clay Math. Proc., vol. 11, Amer. Math. Soc., Providence, RI, 2010, pp. 659–675
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by same author, The noncommutative A A -polynomial of ( − 2 , 3 , n ) (-2,3,n) pretzel knots , Exp. Math. 21
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Stavros Garoufalidis and Thang T. Q. Lê, A survey of q q -holonomic functions , Enseign. Math. 62
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Kannan Soundararajan, Integral factorial ratios: irreducible examples with height larger than 1 , Philos. Trans. Roy. Soc. A 378
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2021
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Stavros Garoufalidis and Christoph Koutschan, In preparation , Preprint 2021
2021
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Sergei Gukov and Ciprian Manolescu, A two-variable series for knot complements , Quantum Topol. 12
2021
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