Asymptotics of the colored Jones polynomial and the A-polynomial

Nuclear Physics B

Volumn 773, Issue 3, 2007, Pages 184-202

  Hikami, Kazuhiro ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34248561163     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2007.03.022     Document Type: Article

References (35)

1. Witten E. Quantum field theory and the Jones polynomial. Commun. Math. Phys. 121 (1989) 351-399
2. Mariño M. Chern-Simons theory and topological strings. Rev. Mod. Phys. 77 (2005) 675-720
3. Kashaev R.M. The hyperbolic volume of knots from quantum dilogarithm. Lett. Math. Phys. 39 (1997) 269-275
4. Murakami H., and Murakami J. The colored Jones polynomials and the simplicial volume of a knot. Acta Math. 186 (2001) 85-104
5. Cooper D., Culler M., Gillet H., Long D.D., and Shalen P.B. Plane curves associated to character varieties of 3-manifolds. Invent. Math. 118 (1994) 47-84
6. Cooper D., and Long D.D. Representation theory and the A-polynomial of a knot-knot theory and its applications. Chaos Solitons Fractals 9 (1998) 749-763
7. Garoufalidis S. On the characteristic and deformation varieties of a knot. Geom. Topol. Monogr. 7 (2004) 291-309
8. Hikami K. Difference equation of the colored Jones polynomial for the torus knot. Int. J. Math. 15 (2004) 959-965
9. Le T.T.Q. The colored Jones polynomial and the A-polynomial of knots. Adv. Math. 207 (2006) 782-804
10. Takata T. The colored Jones polynomial and the A-polynomial for twist knots. math.GT/0401068
11. Gelca R. On the relation between the A-polynomial and the Jones polynomial. Proc. Am. Math. Soc. 130 (2002) 1235-1241
12. Gelca R., and Sain J. The noncommutative A-ideal of a (2, 2 p + 1)-torus knot determines its Jones polynomial. J. Knot Theory Ramifications 12 (2003) 187-202
13. Gukov S. Three-dimensional quantum gravity, Chern-Simons theory, and the A-polynomial. Commun. Math. Phys. 255 (2005) 577-627
14. Murakami H., and Yokota Y. The colored Jones polynomials of the figure-eight knot and its Dehn surgery spaces. math.GT/0401084
15. Garoufalidis S., and Le T.T.Q. The colored Jones function is q-holonomic. Geom. Topol. 9 (2005) 1253-1293
16. Neumann W.D., and Zagier D. Volumes of hyperbolic three-manifolds. Topology 24 (1985) 307-332
17. Yoshida T. The η-invariant of hyperbolic 3-manifolds. Invent. Math. 81 (1985) 473-514
18. Masbaum G. Skein-theoretical derivation of some formulas of Habiro. Algeb. Geom. Topol. 3 (2003) 537-556
19. 2 invariants of knots and integral homology spheres. Geom. Topol. Monogr. 4 (2002) 55-68
20. Hoste J., and Shanahan P.D. A formula for the A-polynomial of twist knots. J. Knot Theory Ramifications 13 (2004) 193-209
21. Andrews G.E. The Theory of Partitions (1976), Addison-Wesley, London
22. Lewin L. Polylogarithms and Associated Functions (1981), North-Holland, New York
23. Richmond B., and Szekeres G. Some formulas related to dilogarithms, the zeta function and the Andrews-Gordon identities. J. Aust. Math. Soc. (Series A) 31 (1981) 362-373
24. Weeks J. SnapPea. http://www.geometrygames.org/SnapPea/
25. Sakuma M., and Weeks J. Examples of canonical decompositions of hyperbolic link complements. Jpn. J. Math. 21 (1995) 393-439
26. Milnor J. Hyperbolic geometry: The first 150 years. Bull. Am. Math. Soc. 6 (1982) 9-24
27. Hikami K. Volume conjecture and asymptotic expansion of q-series. Exp. Math. 12 (2003) 319-337
28. Murakami H. Asymptotic behaviors of the colored Jones polynomials of a torus knot. Int. J. Math 15 (2004) 547-555
29. Zagier D. Vassiliev invariants and a strange identity related to the Dedekind eta-function. Topology 40 (2001) 945-960
30. Hikami K. q-series and L-functions related to half-derivatives of the Andrews-Gordon identity. Ramanujan J. 11 (2006) 175-197
31. Hikami K., and Kirillov A.N. Torus knot and minimal model. Phys. Lett. B 575 (2003) 343-348
32. Hikami K. Quantum invariant for torus link and modular forms. Commun. Math. Phys. 246 (2004) 403-426
33. Hikami K. On the quantum invariant for the Brieskorn homology spheres. Int. J. Math. 16 (2005) 661-685
34. Hikami K., and Kirillov A.N. Hypergeometric generating function of L-function, Slater's identities, and quantum knot invariant. Algebra i Analiz 17 (2005) 190-208
35. Le T.T.Q. Quantum invariants of 3-manifolds: Integrality, splitting, and perturbative expansion. Topol. Appl. 127 (2003) 125-152