Volume 9, issue 3 (2009)

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

Volume 25
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

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
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Quantum Teichmüller space and Kashaev algebra

Ren Guo and Xiaobo Liu

Algebraic & Geometric Topology 9 (2009) 1791–1824
Bibliography
1 H Bai, A uniqueness property for the quantization of Teichmüller spaces, Geom. Dedicata 128 (2007) 1 MR2350143
2 H Bai, F Bonahon, X Liu, Local representations of the quantum Teichmüller space arXiv:0707.2151
3 F Bonahon, Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form, Ann. Fac. Sci. Toulouse Math. $(6)$ 5 (1996) 233 MR1413855
4 F Bonahon, Quantum Teichmüller theory and representations of the pure braid group, Commun. Contemp. Math. 10 (2008) 913 MR2468371
5 F Bonahon, X Liu, Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms, Geom. Topol. 11 (2007) 889 MR2326938
6 L O Chekhov, V V Fock, Observables in 3D gravity and geodesic algebras, Czechoslovak J. Phys. 50 (2000) 1201 MR1806262
7 V V Fock, Dual Teichmüller spaces arXiv:dg-ga/9702018
8 V V Fok, L O Chekhov, Quantum Teichmüller spaces, Teoret. Mat. Fiz. 120 (1999) 511 MR1737362
9 R M Kashaev, Quantization of Teichmüller spaces and the quantum dilogarithm, Lett. Math. Phys. 43 (1998) 105 MR1607296
10 R M Kashaev, The Liouville central charge in quantum Teichmüller theory, Tr. Mat. Inst. Steklova 226 (1999) 72 MR1782553
11 R M Kashaev, On the spectrum of Dehn twists in quantum Teichmüller theory, from: "Physics and combinatorics, 2000 (Nagoya)", World Sci. Publ., River Edge, NJ (2001) 63 MR1872252
12 R M Kashaev, On quantum moduli space of flat $\mathrm{PSL}_2(\mathbb{R})$–connections on a punctured surface, from: "Handbook of Teichmüller theory Vol I", IRMA Lect. Math. Theor. Phys. 11, Eur. Math. Soc., Zürich (2007) 761 MR2349684
13 X Liu, Gromov–Witten invariants and moduli spaces of curves, from: "International Congress of Mathematicians Vol II", Eur. Math. Soc., Zürich (2006) 791 MR2275623
14 X Liu, The quantum Teichmüller space as a non-commutative algebraic object, J. Knot Theory Ramifications 18 (2009) 705
15 R C Penner, The decorated Teichmüller space of punctured surfaces, Comm. Math. Phys. 113 (1987) 299 MR919235
16 J Teschner, An analog of a modular functor from quantized Teichmüller theory, from: "Handbook of Teichmüller theory Vol I", IRMA Lect. Math. Theor. Phys. 11, Eur. Math. Soc., Zürich (2007) 685 MR2349683
17 W P Thurston, The topology and geometry of 3–manifolds, lecture notes, Princeton University (1976–1979)