Volume 13, issue 6 (2013)

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

Volume 23
Issue 9, 3909–4400
Issue 8, 3417–3908
Issue 7, 2925–3415
Issue 6, 2415–2924
Issue 5, 1935–2414
Issue 4, 1463–1934
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Factorization rules in quantum Teichmüller theory

Julien Roger

Algebraic & Geometric Topology 13 (2013) 3411–3446
Bibliography
1 W Abikoff, Augmented Teichmüller spaces, Bull. Amer. Math. Soc. 82 (1976) 333 MR0432919
2 W Abikoff, Degenerating families of Riemann surfaces, Ann. of Math. 105 (1977) 29 MR0442293
3 H Bai, A uniqueness property for the quantization of Teichmüller spaces, Geom. Dedicata 128 (2007) 1 MR2350143
4 H Bai, F Bonahon, X Liu, Local representations of the quantum Teichmüller space arXiv:0707.2151
5 L Bers, Spaces of degenerating Riemann surfaces, from: "Discontinuous groups and Riemann surfaces" (editor L Greenberg), Ann. of Math. Studies 79, Princeton Univ. Press (1974) 43 MR0361051
6 F Bonahon, Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form, Ann. Fac. Sci. Toulouse Math. 5 (1996) 233 MR1413855
7 F Bonahon, X Liu, Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms, Geom. Topol. 11 (2007) 889 MR2326938
8 L D Faddeev, R M Kashaev, Quantum dilogarithm, Modern Phys. Lett. A 9 (1994) 427 MR1264393
9 V V Fock, Dual Teichmüller space arXiv:dg-ga/9702018
10 V V Fock, L O Chekhov, Quantum Teichmüller spaces, Teoret. Mat. Fiz. 120 (1999) 511 MR1737362
11 V V Fock, A B Goncharov, The quantum dilogarithm and representations of quantum cluster varieties, Invent. Math. 175 (2009) 223 MR2470108
12 R M Kashaev, Quantization of Teichmüller spaces and the quantum dilogarithm, Lett. Math. Phys. 43 (1998) 105 MR1607296
13 R M Kashaev, On the spectrum of Dehn twists in quantum Teichmüller theory, from: "Physics and combinatorics" (editors A N Kirillov, N Liskova), World Sci. Publ. (2001) 63 MR1872252
14 X Liu, The quantum Teichmüller space as a noncommutative algebraic object, J. Knot Theory Ramifications 18 (2009) 705 MR2527682
15 H Masur, Extension of the Weil–Petersson metric to the boundary of Teichmuller space, Duke Math. J. 43 (1976) 623 MR0417456
16 R C Penner, The decorated Teichmüller space of punctured surfaces, Comm. Math. Phys. 113 (1987) 299 MR919235
17 J Teschner, On the relation between quantum Liouville theory and the quantized Teichmüller spaces, from: "Proceedings of 6th International Workshop on Conformal Field Theory and Integrable Models", Internat. J. Modern Phys. A 19 (2004) 459 MR2087126
18 J Teschner, An analog of a modular functor from quantized Teichmüller theory, from: "Handbook of Teichmüller theory. Vol. I" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 11, Eur. Math. Soc., Zürich (2007) 685 MR2349683
19 W P Thurston, Minimal stretch maps between hyperbolic surfaces arXiv:math/9801039
20 H Verlinde, Conformal field theory, two-dimensional quantum gravity and quantization of Teichmüller space, Nuclear Phys. B 337 (1990) 652 MR1057726
21 H Verlinde, E Verlinde, Conformal field theory and geometric quantization, from: "Superstrings '89" (editors M Green, R Iengo, S Randjbar-Daemi, E Sezgin, A Strominger), World Sci. Publ. (1990) 422 MR1159975
22 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772
23 S Wolpert, On the Weil–Petersson geometry of the moduli space of curves, Amer. J. Math. 107 (1985) 969 MR796909
24 S Wolpert, The Weil–Petersson metric geometry, from: "Handbook of Teichmüller theory. Vol. II" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 13, Eur. Math. Soc., Zürich (2009) 47 MR2497791