Geometry & Topology Volume 17, issue 3 (2013)

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The quantum content of the gluing equations

Tudor Dimofte and Stavros Garoufalidis

Geometry & Topology 17 (2013) 1253–1315

DOI: 10.2140/gt.2013.17.1253

Bibliography

1	M Aganagic, V Bouchard, A Klemm, Topological strings and (almost) modular forms, Comm. Math. Phys. 277 (2008) 771 MR2365453
2	J Andersen, R Kashaev, A TQFT from quantum Teichmüller theory arXiv:1109.6295
3	D Bar-Natan, E Witten, Perturbative expansion of Chern–Simons theory with noncompact gauge group, Comm. Math. Phys. 141 (1991) 423 MR1133274
4	E W Barnes, The genesis of the double gamma functions, Proc. London Math. Soc. 31 (1899) 358 MR1576719
5	R Benedetti, C Petronio, Branched standard spines of 3–manifolds, 1653, Springer (1997) MR1470454
6	D Bessis, C Itzykson, J B Zuber, Quantum field theory techniques in graphical enumeration, Adv. in Appl. Math. 1 (1980) 109 MR603127
7	D W Boyd, N M Dunfield, F Rodriguez-Villegas, Mahler’s measure and the dilogarithm (II) arXiv:0308041
8	B A Burton, Regina : Normal surface and 3–manifold topology software
9	D Calegari, Real places and torus bundles, Geom. Dedicata 118 (2006) 209 MR2239457
10	B G Casler, An imbedding theorem for connected 3–manifolds with boundary, Proc. Amer. Math. Soc. 16 (1965) 559 MR0178473
11	A A Champanerkar, A–polynomial and Bloch invariants of hyperbolic 3–manifolds, PhD thesis, Columbia University (2003) MR2704573
12	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
13	M Culler, N M Dunfield, J R Weeks, SnapPy, a computer program for studying the geometry and topology of 3–manifolds (2011)
14	J A De Loera, J Rambau, F Santos, Triangulations, 25, Springer (2010) MR2743368
15	T Dimofte, Quantum Riemann surfaces in Chern–Simons theory arXiv:1102.4847
16	T Dimofte, D Gaiotto, S Gukov, Gauge theories labelled by three-manifolds arXiv:1108.4389
17	T Dimofte, S Gukov, J Lenells, D Zagier, Exact results for perturbative Chern–Simons theory with complex gauge group, Commun. Number Theory Phys. 3 (2009) 363 MR2551896
18	J Dubois, Non abelian twisted Reidemeister torsion for fibered knots, Canad. Math. Bull. 49 (2006) 55 MR2198719
19	J Dubois, S Garoufalidis, Rationality of the SL(2, ℂ)–Reidemeister torsion in dimension 3 arXiv:0908.1690
20	N M Dunfield, Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds, Invent. Math. 136 (1999) 623 MR1695208
21	N M Dunfield, S Friedl, N Jackson, Twisted Alexander polynomials of hyperbolic knots, Exp. Math. 21 (2012) 329 MR3004250
22	N M Dunfield, S Garoufalidis, Incompressibility criteria for spun-normal surfaces, Trans. Amer. Math. Soc. 364 (2012) 6109 MR2946944
23	J L Dupont, C H Sah, Scissors congruences, II, J. Pure Appl. Algebra 25 (1982) 159 MR662760
24	J L Dupont, C K Zickert, A dilogarithmic formula for the Cheeger–Chern–Simons class, Geom. Topol. 10 (2006) 1347 MR2255500
25	D B A Epstein, R C Penner, Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988) 67 MR918457
26	B Eynard, Invariants of spectral curves and intersection theory of moduli spaces of complex curves arXiv:1110.2949
27	L D Faddeev, Discrete Heisenberg–Weyl group and modular group, Lett. Math. Phys. 34 (1995) 249 MR1345554
28	L D Faddeev, R M Kashaev, Quantum dilogarithm, Modern Phys. Lett. A 9 (1994) 427 MR1264393
29	L D Faddeev, R M Kashaev, A Y Volkov, Strongly coupled quantum discrete Liouville theory. I. Algebraic approach and duality, Comm. Math. Phys. 219 (2001) 199 MR1828812
30	V V Fok, L O Chekhov, Quantum Teichmüller spaces, Teoret. Mat. Fiz. 120 (1999) 511 MR1737362
31	S Garoufalides, D Zagier, Empirical relations betwen q–series and Kashaev’s invariant of knots, Preprint (2013)
32	S Garoufalidis, Quantum knot invariants, Mathematische Arbeitstagung talk 2011 arXiv:1201.3314
33	S Garoufalidis, On the characteristic and deformation varieties of a knot, from: "Proceedings of the Casson Fest", Geom. Topol. Monogr. 7 (2004) 291 MR2172488
34	S Garoufalidis, Chern–Simons theory, analytic continuation and arithmetic, Acta Math. Vietnam. 33 (2008) 335 MR2501849
35	S Garoufalidis, C D Hodgson, J H Rubinstein, H Segerman, 1–efficient triangulations and the index of a cusped hyperbolic 3–manifold arXiv:1303.5278
36	S Garoufalidis, T T Q Lê, Asymptotics of the colored Jones function of a knot, Geom. Topol. 15 (2011) 2135 MR2860990
37	S Garoufalidis, D Zagier, Asymptotics of quantum knot invariants, Preprint (2013)
38	S Goette, C K Zickert, The extended Bloch group and the Cheeger–Chern–Simons class, Geom. Topol. 11 (2007) 1623 MR2350461
39	S Gukov, Three-dimensional quantum gravity, Chern–Simons theory, and the A–polynomial, Comm. Math. Phys. 255 (2005) 577 MR2134725
40	S Gukov, H Murakami, SL(2, ℂ) Chern–Simons theory and the asymptotic behavior of the colored Jones polynomial, Lett. Math. Phys. 86 (2008) 79 MR2465747
41	S Gukov, P Sułkowski, A–polynomial, B–model, and quantization, J. High Energy Phys. (2012) 070 MR2996110
42	K Hikami, Hyperbolic structure arising from a knot invariant, Internat. J. Modern Phys. A 16 (2001) 3309 MR1848458
43	K Hikami, Generalized volume conjecture and the A–polynomials : the Neumann–Zagier potential function as a classical limit of the partition function, J. Geom. Phys. 57 (2007) 1895 MR2330673
44	C D Hodgson, J H Rubinstein, H Segerman, Triangulations of hyperbolic 3–manifolds admitting strict angle structures arXiv:1111.3168
45	K Hori, S Katz, A Klemm, R Pandharipande, R Thomas, C Vafa, R Vakil, E Zaslow, Mirror symmetry, 1, Amer. Math. Soc. (2003) MR2003030
46	V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. 126 (1987) 335 MR908150
47	E Kang, Normal surfaces in non-compact 3–manifolds, J. Aust. Math. Soc. 78 (2005) 305 MR2142159
48	E Kang, J H Rubinstein, Ideal triangulations of 3–manifolds, I : Spun normal surface theory, from: "Proceedings of the Casson Fest" (editors C Gordon, Y Rieck), Geom. Topol. Monogr. 7 (2004) 235 MR2172486
49	R M Kashaev, Quantum dilogarithm as a 6j–symbol, Modern Phys. Lett. A 9 (1994) 3757 MR1317945
50	R M Kashaev, A link invariant from quantum dilogarithm, Modern Phys. Lett. A 10 (1995) 1409 MR1341338
51	R M Kashaev, Quantization of Teichmüller spaces and the quantum dilogarithm, Lett. Math. Phys. 43 (1998) 105 MR1607296
52	S V Matveev, Transformations of special spines, and the Zeeman conjecture, Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987) 1104, 1119 MR925096
53	S Matveev, Algorithmic topology and classification of 3–manifolds, 9, Springer (2007) MR2341532
54	W Müller, Analytic torsion and R–torsion for unimodular representations, J. Amer. Math. Soc. 6 (1993) 721 MR1189689
55	H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85 MR1828373
56	W D Neumann, Combinatorics of triangulations and the Chern–Simons invariant for hyperbolic 3–manifolds, from: "Topology ’90" (editors B Apanasov, W D Neumann, A W Reid, L Siebenmann), Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 243 MR1184415
57	W D Neumann, Extended Bloch group and the Cheeger–Chern–Simons class, Geom. Topol. 8 (2004) 413 MR2033484
58	W D Neumann, D Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307 MR815482
59	R Piergallini, Standard moves for standard polyhedra and spines, Rend. Circ. Mat. Palermo Suppl. (1988) 391 MR958750
60	M Polyak, Feynman diagrams for pedestrians and mathematicians, from: "Graphs and patterns in mathematics and theoretical physics" (editors M Lyubich, L Takhtajan), Proc. Sympos. Pure Math. 73, Amer. Math. Soc. (2005) 15 MR2131010
61	B Ponsot, J Teschner, Clebsch-Gordan and Racah–Wigner coefficients for a continuous series of representations of 𝒰_q(sl(2, ℝ)), Comm. Math. Phys. 224 (2001) 613 MR1871903
62	J Porti, Torsion de Reidemeister pour les variétés hyperboliques, Mem. Amer. Math. Soc. 128 (1997) MR1396960
63	D B Ray, I M Singer, R–torsion and the Laplacian on Riemannian manifolds, Advances in Math. 7 (1971) 145 MR0295381
64	D Shale, Linear symmetries of free boson fields, Trans. Amer. Math. Soc. 103 (1962) 149 MR0137504
65	V P Spiridonov, G S Vartanov, Elliptic hypergeometry of supersymmetric dualities II : orthogonal groups, knots, and vortices arXiv:1107.5788
66	W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)
67	W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982) 357 MR648524
68	S Tillmann, Normal surfaces in topologically finite 3–manifolds, Enseign. Math. 54 (2008) 329 MR2478091
69	S Tillmann, Degenerations of ideal hyperbolic triangulations, Math. Z. 272 (2012) 793 MR2995140
70	V G Turaev, The Yang–Baxter equation and invariants of links, Invent. Math. 92 (1988) 527 MR939474
71	A Weil, Sur certains groupes d’opérateurs unitaires, Acta Math. 111 (1964) 143 MR0165033
72	E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772
73	E Witten, Quantization of Chern–Simons gauge theory with complex gauge group, Comm. Math. Phys. 137 (1991) 29 MR1099255
74	Y Yamaguchi, A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion, Ann. Inst. Fourier (Grenoble) 58 (2008) 337 MR2401224
75	C K Zickert, The volume and Chern–Simons invariant of a representation, Duke Math. J. 150 (2009) 489 MR2582103