Volume 11, issue 3 (2007)

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$6j$–symbols, hyperbolic structures and the volume conjecture

Francesco Costantino

Geometry & Topology 11 (2007) 1831–1854
Bibliography
1 S Baseilhac, R Benedetti, Quantum hyperbolic invariants of $3$–manifolds with $\mathrm{PSL}(2,\mathbb C)$–characters, Topology 43 (2004) 1373 MR2081430
2 S Baseilhac, R Benedetti, Classical and quantum dilogarithmic invariants of flat $\mathrm{PSL}(2,\mathbb{C})$–bundles over $3$–manifolds, Geom. Topol. 9 (2005) 493 MR2140989
3 S Baseilhac, R Benedetti, Quantum hyperbolic geometry (2006) arXiv:math.GT/0611504
4 F Costantino, Colored Jones invariants of links in $\#S^2 \times S^1$ and the volume conjecture (2007)
5 F Costantino, D P Thurston, $3$–manifolds efficiently bound $4$–manifolds (2005) arXiv:math.GT/0506577
6 P Doyle, G Leibon, 23040 symmetries of hyperbolic tetrahedra (2003) arXiv:math.GT/0309187
7 R Frigerio, C Petronio, Construction and recognition of hyperbolic $3$–manifolds with geodesic boundary, Trans. Amer. Math. Soc. 356 (2004) 3243 MR2052949
8 S Garoufalidis, T Le, Asymptotics of the colored Jones function of a knot (2007) arXiv:math.GT/0508100
9 S Gukov, Three-dimensional quantum gravity, Chern–Simons theory, and the A–polynomial, Comm. Math. Phys. 255 (2005) 577 MR2134725
10 R M Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39 (1997) 269 MR1434238
11 R M Kashaev, O Tirkkonen, A proof of the volume conjecture on torus knots, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 269 (2000) 262, 370 MR1805865
12 J Milnor, Hyperbolic geometry: the first 150 years, Bull. Amer. Math. Soc. (N.S.) 6 (1982) 9 MR634431
13 Y Mohanty, The Regge symmetry is a scissors congruence in hyperbolic space, Algebr. Geom. Topol. 3 (2003) 1 MR1997312
14 H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85 MR1828373
15 H Murakami, J Murakami, Asymptotic behaviors of the colored Jones polynomial of a torus knot (2004) arXiv:math.GT/0405126
16 H Murakami, J Murakami, M Okamoto, T Takata, Y Yokota, Kashaev's conjecture and the Chern–Simons invariants of knots and links, Experiment. Math. 11 (2002) 427 MR1959752
17 H Murakami, Y Yokota, The colored Jones polynomial of the figure eight knot and its Dehn surgery spaces arXiv:math.GT/0401084
18 J Murakami, M Yano, On the volume of a hyperbolic and spherical tetrahedron, Comm. Anal. Geom. 13 (2005) 379 MR2154824
19 W D Neumann, D Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307 MR815482
20 J Roberts, Classical $6j$–symbols and the tetrahedron, Geom. Topol. 3 (1999) 21 MR1673272
21 Y U Taylor, C T Woodward, $6j$ symbols for $U_q(sl_2)$ and non-Euclidean tetrahedra, Selecta Math. (N.S.) 11 (2005) 539 MR2215264
22 W P Thurston, The geometry and topology of three manifolds
23 V G Turaev, Quantum invariants of knots and $3$–manifolds, de Gruyter Studies in Mathematics 18, Walter de Gruyter & Co. (1994) MR1292673
24 A Ushijima, A volume formula for generalised hyperbolic tetrahedra, from: "Non-Euclidean geometries", Math. Appl. (N. Y.) 581, Springer (2006) 249 MR2191251
25 R Van der Veen, The volume conjecture for Whitehead chains (2006) arXiv:math.GT/0611181
26 H Zheng, Proof of the volume conjecture for Whitehead doubles of a family of torus knots (2005) arXiv:math.GT/0508138