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This is a survey talk on one of the best known quantum knot invariants, the colored Jones polynomial of a knot, and its relation to the algebraic/geometric topology and hyperbolic geometry of the knot complement.
Wolfgang Haken, Theorie der Normalflächen , Acta Math. 105
1961
Earlier work this paper cites.
Dale Rolfsen, Knots and links , Mathematics Lecture Series, vol. 7, Publish or Perish Inc., Houston, TX, 1990, Corrected reprint of the 1976 original
1976
Earlier work this paper cites.
William Thurston, The geometry and topology of 3-manifolds , Universitext, Springer-Verlag, Berlin, 1977, Lecture notes, Princeton
1977
Earlier work this paper cites.
Carl M. Bender and Steven A. Orszag, Advanced mathematical methods for scientists and engineers. I , Springer-Verlag, New York, 1999, Asymptotic methods and perturbation theory, Reprint of the 1978 original
1978
Earlier work this paper cites.
A. Hatcher, On the boundary curves of incompressible surfaces. , Pacific J. Math. 99
1982
Earlier work this paper cites.
V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials , Ann. of Math. (2) 126
1987
Earlier work this paper cites.
V. G. Turaev, The Yang-Baxter equation and invariants of links , Invent. Math. 92
1988
Earlier work this paper cites.
Edward Witten, Quantum field theory and the Jones polynomial , Comm. Math. Phys. 121
1989
Earlier work this paper cites.
Doron Zeilberger, A holonomic systems approach to special functions identities , J. Comput. Appl. Math. 32
1990
Earlier work this paper cites.
Herbert S. Wilf and Doron Zeilberger, An algorithmic proof theory for hypergeometric (ordinary and “ q q ”) multisum/integral identities , Invent. Math. 108
1992
Earlier work this paper cites.
W. Nahm, A. Recknagel, and M. Terhoeven, Dilogarithm identities in conformal field theory , Modern Phys. Lett. A 8
1993
Earlier work this paper cites.
D. Cooper, M. Culler, H. Gillet, D. D. Long, and P. B. Shalen, Plane curves associated to character varieties of 3 3 -manifolds , Invent. Math. 118
1994
Earlier work this paper cites.
Louis H. Kauffman and Sóstenes L. Lins, Temperley-Lieb recoupling theory and invariants of 3 3 -manifolds , Annals of Mathematics Studies, vol. 134, Princeton University Press, Princeton, NJ, 1994
1994
Earlier work this paper cites.
by same author, Quantum invariants of knots and 3-manifolds , de Gruyter Studies in Mathematics, vol. 18, Walter de Gruyter & Co., Berlin, 1994
1994
Earlier work this paper cites.
Dror Bar-Natan and Stavros Garoufalidis, On the Melvin-Morton-Rozansky conjecture , Invent. Math. 125
1996
Earlier work this paper cites.
Jens Carsten Jantzen, Lectures on quantum groups , Graduate Studies in Mathematics, vol. 6, American Mathematical Society, Providence, RI, 1996
1996
Earlier work this paper cites.
Marko Petkovšek, Herbert S. Wilf, and Doron Zeilberger, A = B A=B , A K Peters Ltd., Wellesley, MA, 1996, With a foreword by Donald E. Knuth, With a separately available computer disk
1996
Earlier work this paper cites.
R. M. Kashaev, The hyperbolic volume of knots from the quantum dilogarithm , Lett. Math. Phys. 39
1997
Earlier work this paper cites.
Hitoshi Murakami and Jun Murakami, The colored Jones polynomials and the simplicial volume of a knot , Acta Math. 186
2001
Earlier work this paper cites.
Don Zagier, Vassiliev invariants and a strange identity related to the Dedekind eta-function , Topology 40
2001
Earlier work this paper cites.
Răzvan Gelca, On the relation between the A A -polynomial and the Jones polynomial , Proc. Amer. Math. Soc. 130
2002
Earlier work this paper cites.
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)
2002
Earlier work this paper cites.
Colin Maclachlan and Alan W. Reid, The arithmetic of hyperbolic 3-manifolds , Graduate Texts in Mathematics, vol. 219, Springer-Verlag, New York, 2003
2003
Cited alongside, same era.
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 (electronic)
2004
Cited alongside, same era.
Jim Hoste and Patrick D. Shanahan, A formula for the A-polynomial of twist knots , J. Knot Theory Ramifications 13
2004
Cited alongside, same era.
Hitoshi Murakami, Some limits of the colored Jones polynomials of the figure-eight knot , Kyungpook Math. J. 44
2004
Cited alongside, same era.
Walter D. Neumann, Extended Bloch group and the Cheeger-Chern-Simons class , Geom. Topol. 8
2004
Cited alongside, same era.
Tudor Dimofte, Quantum Riemann surfaces in Chern-Simons theory , arXiv:1102.4847
2011
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David Futer, Efstratia Kalfagianni, and Jessica S. Purcell, Slopes and colored Jones polynomials of adequate knots , Proc. Amer. Math. Soc. 139
2011
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Stavros Garoufalidis, The degree of a q q -holonomic sequence is a quadratic quasi-polynomial , Electron. J. Combin. 18
2011
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by same author, The Jones slopes of a knot , Quantum Topol. 2
2011
Later among the works it cites.
by same author, Knots and tropical curves , Interactions between hyperbolic geometry, quantum topology and number theory, Contemp. Math., vol. 541, Amer. Math. Soc., Providence, RI, 2011, pp. 83–101
2011
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Dror Bar-Natan, Knotatlas , 2005, http://katlas.org
2005
Cited alongside, same era.
Stavros Garoufalidis and Thang T. Q. Lê, The colored Jones function is q q -holonomic , Geom. Topol. 9
2005
Cited alongside, same era.
Sergei Gukov, Three-dimensional quantum gravity, Chern-Simons theory, and the A-polynomial , Comm. Math. Phys. 255
2005
Cited alongside, same era.
Thang T. Q. Lê, The colored Jones polynomial and the A A -polynomial of knots , Adv. Math. 207
2006
Cited alongside, same era.
Sebastian Goette and Christian K. Zickert, The extended Bloch group and the Cheeger-Chern-Simons class , Geom. Topol. 11
2007
Cited alongside, same era.
by same author, The dilogarithm function , Frontiers in number theory, physics, and geometry. II, Springer, Berlin, 2007, pp. 3–65
2007
Cited alongside, same era.
Stavros Garoufalidis, Chern-Simons theory, analytic continuation and arithmetic , Acta Math. Vietnam. 33
2008
Cited alongside, same era.
by same author, Asymptotics of the colored Jones function of a knot , Geom. Topol. 15
2011
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by same author, Nahm sums, stability and the colored Jones polynomial , 2011, arXiv:1112.3905
2011
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Stavros Garoufalidis and Thomas W. Mattman, The A A -polynomial of the ( − 2 , 3 , 3 + 2 n ) (-2,3,3+2n) pretzel knots , New York J. Math. 17
2011
Later among the works it cites.
Maxim Kontsevich and Yan Soibelman, Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants , Commun. Number Theory Phys. 5
2011
Later among the works it cites.
Masha Vlasenko and Sander Zwegers, Nahm’s conjecture: asymptotic computations and counterexamples , Commun. Number Theory Phys. 5
2011
Later among the works it cites.
by same author, The quantum content of the gluing equations , arXiv:1202.6268
2012
Closest in time.
Nathan M. Dunfield and Stavros Garoufalidis, Incompressibility criteria for spun-normal surfaces , Trans. Amer. Math. Soc. 364
2012
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Stavros Garoufalidis, Alexander Its, Andrei Kapaev, and Marcos Mariño, Asymptotics of the instantons of Painlevé I , Int. Math. Res. Not. IMRN (2012), no. 3, 561–606
2012
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Stavros Garoufalidis and Christoph Koutschan, The noncommutative A A -polynomial of ( − 2 , 3 , n ) (-2,3,n) pretzel knots , Exp. Math. 21
2012
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Stavros Garoufalidis and Christoph Koutschan, Twisting q-holonomic sequences by complex roots of unity , ISSAC, 2012, pp. 179–186
2012
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Stavros Garoufalidis and Roland van der Veen, Asymptotics of quantum spin networks at a fixed root of unity , Math. Ann. 352
2012
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Thang T. Q. Lê and Anh T. Tran, On the AJ conjecture for knots , arXiv:1111.5258
2012
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Anh T. Tran, Proof of a stronger version of the AJ conjecture for torus knots , arXiv:1111.5065
2012
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by same author, Fivebranes and knots , Quantum Topol. 3
2012
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Stavros Garoufalidis and Don Zagier, Asymptotics of quantum knot invariants , Preprint 2013
2013
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by same author, Empirical relations between q q -series and kashaev’s invariant of knots , Preprint 2013
2013
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