Volume 15, issue 4 (2015)

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Analytic families of quantum hyperbolic invariants

Stéphane Baseilhac and Riccardo Benedetti

Algebraic & Geometric Topology 15 (2015) 1983–2063
Bibliography
1 H Bai, Quantum Teichmüller spaces and Kashaev's $6j$–symbols, Algebr. Geom. Topol. 7 (2007) 1541 MR2366170
2 H Bai, F Bonahon, X Liu, Local representations of the quantum Teichmüller space, (2007) arXiv:math.GT/0707
3 S Baseilhac, R Benedetti, Quantum hyperbolic invariants of $3$–manifolds with $\mathrm{PSL}(2,\mathbb C)$–characters, Topology 43 (2004) 1373 MR2081430
4 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
5 S Baseilhac, R Benedetti, Quantum hyperbolic geometry, Algebr. Geom. Topol. 7 (2007) 845 MR2336244
6 S Baseilhac, R Benedetti, The Kashaev and quantum hyperbolic link invariants, J. Gökova Geom. Topol. 5 (2011) 31 MR2872550
7 R Benedetti, C Petronio, Lectures on hyperbolic geometry, Springer (1992) MR1219310
8 R Benedetti, C Petronio, Branched standard spines of $3$–manifolds, Lecture Notes in Mathematics 1653, Springer (1997) MR1470454
9 R Benedetti, C Petronio, Spin structures on $3$–manifolds via arbitrary triangulations, Algebr. Geom. Topol. 14 (2014) 1005 MR3180826
10 S Boyer, X Zhang, On Culler–Shalen seminorms and Dehn filling, Ann. of Math. 148 (1998) 737 MR1670053
11 D Bullock, Rings of $\mathrm{SL}_2(\mathbf{C})$–characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997) 521 MR1600138
12 A A Champanerkar, A–polynomial and Bloch invariants of hyperbolic $3$–manifolds, PhD thesis, Columbia University (2003) MR2704573
13 Y E Choi, Positively oriented ideal triangulations on hyperbolic three-manifolds, Topology 43 (2004) 1345 MR2081429
14 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
15 F Costantino, A calculus for branched spines of $3$–manifolds, Math. Z. 251 (2005) 427 MR2191035
16 M Culler, P B Shalen, Varieties of group representations and splittings of $3$–manifolds, Ann. of Math. 117 (1983) 109 MR683804
17 N M Dunfield, Mahler's measure and the dilogarithm, II, arXiv:math.NT/0308041
18 N M Dunfield, Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds, Invent. Math. 136 (1999) 623 MR1695208
19 S Francaviglia, Hyperbolic volume of representations of fundamental groups of cusped $3$–manifolds, Int. Math. Res. Not. 2004 (2004) 425 MR2040346
20 D Gabai, R Meyerhoff, P Milley, Minimum volume cusped hyperbolic three-manifolds, J. Amer. Math. Soc. 22 (2009) 1157 MR2525782
21 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
22 M Kapovich, Hyperbolic manifolds and discrete groups, Birkhäuser (2009) MR2553578
23 R M Kashaev, Quantum dilogarithm as a $6j$–symbol, Modern Phys. Lett. A 9 (1994) 3757 MR1317945
24 R M Kashaev, A link invariant from quantum dilogarithm, Modern Phys. Lett. A 10 (1995) 1409 MR1341338
25 P Kirk, E Klassen, Chern–Simons invariants of $3$–manifolds decomposed along tori and the circle bundle over the representation space of $T^2$, Comm. Math. Phys. 153 (1993) 521 MR1218931
26 S Lang, Algebraic number theory, Graduate Texts in Mathematics 110, Springer (1994) MR1282723
27 F Luo, S Schleimer, S Tillmann, Geodesic ideal triangulations exist virtually, Proc. Amer. Math. Soc. 136 (2008) 2625 MR2390535
28 F Luo, S Tillmann, T Yang, Thurston's spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic $3$–manifolds, Proc. Amer. Math. Soc. 141 (2013) 335 MR2988735
29 S V Matveev, A T Fomenko, Isoenergetic surfaces of Hamiltonian systems, the enumeration of three-dimensional manifolds in order of growth of their complexity, and the calculation of the volumes of closed hyperbolic manifolds, Uspekhi Mat. Nauk 43 (1988) 5, 247 MR937017
30 H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85 MR1828373
31 W D Neumann, Combinatorics of triangulations and the Chern–Simons invariant for hyperbolic $3$–manifolds, from: "Topology '90", Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 243 MR1184415
32 W D Neumann, Extended Bloch group and the Cheeger–Chern–Simons class, Geom. Topol. 8 (2004) 413 MR2033484
33 W D Neumann, D Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307 MR815482
34 C Petronio, J Porti, Negatively oriented ideal triangulations and a proof of Thurston's hyperbolic Dehn filling theorem, Expo. Math. 18 (2000) 1 MR1751141
35 P B Shalen, Representations of $3$–manifold groups, from: "Handbook of geometric topology", North-Holland (2002) 955 MR1886685
36 J R Weeks, Hyperbolic structures on three-manifolds (Dehn surgery, knot, volume), PhD thesis, Princeton University (1985) MR2634492
37 T Yoshida, The $\eta$–invariant of hyperbolic $3$–manifolds, Invent. Math. 81 (1985) 473 MR807069