Volume 13, issue 6 (2013)

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

Volume 21
Issue 4, 1595–2140
Issue 3, 1075–1593
Issue 2, 543–1074
Issue 1, 1–541

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