Volume 15, issue 4 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Asymptotics of the colored Jones function of a knot

Stavros Garoufalidis and Thang T Q Lê

Geometry & Topology 15 (2011) 2135–2180
Bibliography
1 I Agol, P A Storm, W P Thurston, Lower bounds on volumes of hyperbolic Haken $3$-manifolds, J. Amer. Math. Soc. 20 (2007) 1053 MR2328715
2 G E Andrews, The theory of partitions, Cambridge Math. Library, Cambridge Univ. Press (1998) MR1634067
3 D Bar-Natan, S Garoufalidis, On the Melvin–Morton–Rozansky conjecture, Invent. Math. 125 (1996) 103 MR1389962
4 D Cooper, M Culler, H Gillet, D D Long, P B Shalen, Plane curves associated to character varieties of $3$–manifolds, Invent. Math. 118 (1994) 47 MR1288467
5 N Dunfield, Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds, Invent. Math. 136 (1999) 623 MR1695208
6 J L Dupont, C K Zickert, A dilogarithmic formula for the Cheeger–Chern–Simons class, Geom. Topol. 10 (2006) 1347 MR2255500
7 S Garoufalidis, Beads: from Lie algebras to Lie groups arXiv:math.GT/0201056
8 S Garoufalidis, J S Geronimo, Asymptotics of $q$–difference equations, from: "Primes and knots" (editors T Kohno, M Morishita), Contemp. Math. 416, Amer. Math. Soc. (2006) 83 MR2276137
9 S Garoufalidis, A Kricker, A rational noncommutative invariant of boundary links, Geom. Topol. 8 (2004) 115 MR2033481
10 S Garoufalidis, T T Q Lê, The colored Jones function is $q$–holonomic, Geom. Topol. 9 (2005) 1253 MR2174266
11 S Garoufalidis, L Rozansky, The loop expansion of the Kontsevich integral, the null-move and $S$–equivalence, Topology 43 (2004) 1183 MR2080000
12 S Garoufalidis, X Sun, The $C$–polynomial of a knot, Algebr. Geom. Topol. 6 (2006) 1623 MR2253459
13 S Gukov, Three-dimensional quantum gravity, Chern–Simons theory, and the A-polynomial, Comm. Math. Phys. 255 (2005) 577 MR2134725
14 K Habiro, On the colored Jones polynomials of some simple links, from: "Recent progress towards the volume conjecture (Japanese) (Kyoto, 2000)", Sūrikaisekikenkyūsho Kōkyūroku 1172 (2000) 34 MR1805727
15 K Habiro, A unified Witten–Reshetikhin–Turaev invariant for integral homology spheres, Invent. Math. 171 (2008) 1 MR2358055
16 E Hille, Analytic function theory, Vol. II, Intro. to Higher Math., Ginn and Co. (1962) MR0201608
17 V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. $(2)$ 126 (1987) 335 MR908150
18 R M Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39 (1997) 269 MR1434238
19 R Kirby, P Melvin, The $3$–manifold invariants of Witten and Reshetikhin–Turaev for $\mathrm{sl}(2,\mathbf{C})$, Invent. Math. 105 (1991) 473 MR1117149
20 M Lackenby, The volume of hyperbolic alternating link complements, Proc. London Math. Soc. $(3)$ 88 (2004) 204 MR2018964
21 T T Q Lê, Integrality and symmetry of quantum link invariants, Duke Math. J. 102 (2000) 273 MR1749439
22 T T Q Lê, The colored Jones polynomial and the $A$–polynomial of knots, Adv. Math. 207 (2006) 782 MR2271986
23 K Mahler, An application of Jensen's formula to polynomials, Mathematika 7 (1960) 98 MR0124467
24 H Murakami, Some limits of the colored Jones polynomials of the figure-eight knot, Kyungpook Math. J. 44 (2004) 369 MR2095421
25 H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85 MR1828373
26 F W J Olver, Asymptotics and special functions, AKP Classics, A K Peters Ltd. (1997) MR1429619
27 J G Ratcliffe, Foundations of hyperbolic manifolds, Graduate Texts in Math. 149, Springer (2006) MR2249478
28 N Y Reshetikhin, V G Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990) 1 MR1036112
29 L Rozansky, A universal $U(1)$–rcc invariant of links and rationality conjecture arXiv:math.GT/0201139
30 L Rozansky, The universal $R$–matrix, Burau representation, and the Melvin–Morton expansion of the colored Jones polynomial, Adv. Math. 134 (1998) 1 MR1612375
31 J L Schiff, Normal families, Universitext, Springer (1993) MR1211641
32 W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)
33 V G Turaev, Quantum invariants of knots and $3$–manifolds, de Gruyter Studies in Math. 18, de Gruyter (1994) MR1292673
34 R van der Veen, Proof of the volume conjecture for Whitehead chains, Acta Math. Vietnam. 33 (2008) 421 MR2501851
35 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772