Volume 7, issue 2 (2007)

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Quantum hyperbolic geometry

Stephane Baseilhac and Riccardo Benedetti

Algebraic & Geometric Topology 7 (2007) 845–917
Bibliography
1 W Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Mathematics 820, Springer (1980) MR590044
2 M Atiyah, Topological quantum field theories, Inst. Hautes Études Sci. Publ. Math. (1988) MR1001453
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, Teichmüller space and cylinders in quantum hyperbolic field theories, from: "Handbook on Teichmüller Theory" (editor A Papadopoulos), EMS Publishing House (2008)
6 R Benedetti, F Bonsante, Canonical Wick rotations in 3–dimensional gravity, to appear in Mem. Amer. Math. Soc. arXiv:math.DG/0508485
7 R Benedetti, C Petronio, Lectures on hyperbolic geometry, Universitext, Springer (1992) MR1219310
8 F Bonahon, Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form, Ann. Fac. Sci. Toulouse Math. $(6)$ 5 (1996) 233 MR1413855
9 F Bonahon, X Liu, Representations of the quantum Teichmuller space and invariants of surface diffeomorphisms arXiv:math.GT/0407086
10 R D Canary, D B A Epstein, P Green, Notes on notes of Thurston, from: "Analytical and geometric aspects of hyperbolic space (Coventry/Durham, 1984)", London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press (1987) 3 MR903850
11 A Champanerkar, A-polynomial and Bloch invariants of hyperbolic $3$-manifolds, PhD thesis, Columbia University (2003)
12 Y E Choi, Positively oriented ideal triangulations on hyperbolic three-manifolds, Topology 43 (2004) 1345 MR2081429
13 J L Dupont, C K Zickert, A dilogarithmic formula for the Cheeger-Chern-Simons class, Geom. Topol. 10 (2006) 1347 MR2255500
14 D B A Epstein, A Marden, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, from: "Analytical and geometric aspects of hyperbolic space (Coventry/Durham, 1984)", London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press (1987) 113 MR903852
15 W Floyd, A Hatcher, Incompressible surfaces in punctured-torus bundles, Topology Appl. 13 (1982) 263 MR651509
16 S Francaviglia, Algebraic and geometric solutions of hyperbolicity equations, Topology Appl. 145 (2004) 91 MR2100867
17 S Francaviglia, Hyperbolic volume of representations of fundamental groups of cusped 3-manifolds, Int. Math. Res. Not. (2004) 425 MR2040346
18 F González-Acuña, J M Montesinos-Amilibia, On the character variety of group representations in $\mathrm{SL}(2,\mathbb{C})$ and $\mathrm{PSL}(2,\mathbb{C})$, Math. Z. 214 (1993) 627 MR1248117
19 M Heusener, J Porti, The variety of characters in $PSL(2,\mathbb{C})$ arXiv:math.GT/0302075
20 R M Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39 (1997) 269 MR1434238
21 R M Kashaev, Coordinates for the moduli space of flat $\mathrm{PSL}(2,\mathbb{R})$-connections, Math. Res. Lett. 12 (2005) 23 MR2122727
22 M Lackenby, The canonical decomposition of once-punctured torus bundles, Comment. Math. Helv. 78 (2003) 363 MR1988201
23 W D Neumann, Combinatorics of triangulations and the Chern-Simons invariant for hyperbolic $3$-manifolds, from: "Topology '90 (Columbus, OH, 1990)", Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 243 MR1184415
24 W D Neumann, Extended Bloch group and the Cheeger-Chern-Simons class, Geom. Topol. 8 (2004) 413 MR2033484
25 A Papadopoulos, R C Penner, La forme symplectique de Weil-Petersson et le bord de Thurston de l'espace de Teichmüller, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991) 871 MR1108510
26 R C Penner, The decorated Teichmüller space of punctured surfaces, Comm. Math. Phys. 113 (1987) 299 MR919235
27 C Petronio, J Porti, Negatively oriented ideal triangulations and a proof of Thurston's hyperbolic Dehn filling theorem, Expo. Math. 18 (2000) 1 MR1751141
28 R Riley, Nonabelian representations of $2$-bridge knot groups, Quart. J. Math. Oxford Ser. $(2)$ 35 (1984) 191 MR745421
29 Y Sözen, F Bonahon, The Weil-Petersson and Thurston symplectic forms, Duke Math. J. 108 (2001) 581 MR1838662
30 W Thurston, The Geometry and Topology of Three-Manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)
31 V G Turaev, Homotopy field theory in dimension 3 and crossed group-categories arXiv:math.GT/0005291
32 V G Turaev, Quantum invariants of knots and 3-manifolds, de Gruyter Studies in Mathematics 18, Walter de Gruyter & Co. (1994) MR1292673
33 V G Turaev, O Y Viro, State sum invariants of $3$-manifolds and quantum $6j$-symbols, Topology 31 (1992) 865 MR1191386