Algebraic & Geometric Topology Volume 7, issue 3 (2007)

Download this article
	For screen
	For printing

Recent 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 spaces and Kashaev's $6j$–symbols

Hua Bai

Algebraic & Geometric Topology 7 (2007) 1541–1560

DOI: 10.2140/agt.2007.7.1541

Bibliography

1	H Bai, A uniqueness property for the quantization of Teichmüller spaces (2005) arXiv:math.GT/0509679
2	H Bai, Quantum hyperbolic geometry in dimensions 2 and 3, PhD thesis, University of Southern California (2006)
3	H Bai, F Bonahon, X Liu, Local representations of the quantum Teichmüller space (2007) arXiv:0707.2151
4	S Baseilhac, Dilogarithme quantique et invariants de variétès de dimension trois, PhD thesis, Thèse, Université Paul Sabatier, Toulouse, France (2001)
5	S Baseilhac, R Benedetti, Quantum Hyperbolic State Sum Invariants of 3–Manifolds (2001) arXiv:math.GT/0101234
6	S Baseilhac, R Benedetti, Quantum hyperbolic invariants of 3–manifolds with $\mathrm{ PSL}(2,\mathbb{C})$–characters, Topology 43 (2004) 1373 MR2081430
7	F Bonahon, X Liu, Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms, Geometry & Topology 11 (2007) 889 MR2326938
8	V Chari, A Pressley, A guide to quantum groups, Cambridge University Press (1994) MR1300632
9	F Costantino, $6j$–symbols, hyperbolic structures and the volume conjecture (2006) arXiv:math.GT/0611399
10	V Fock, Dual Teichmüller spaces (1997) arXiv:DG-GA/9702018
11	V V Fock, L O Chekhov, Quantum Teichmüller spaces, Teoret. Mat. Fiz. 120 (1999) 511 MR1737362
12	S Gukov, Three-dimensional quantum gravity, Chern–Simons theory, and the A–polynomial, Comm. Math. Phys. 255 (2005) 577 MR2134725
13	R M Kashaev, A link invariant from quantum dilogarithm, Modern Phys. Lett. A 10 (1995) 1409 MR1341338
14	R M Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39 (1997) 269 MR1434238
15	R M Kashaev, Quantization of Teichmüller spaces and the quantum dilogarithm, Lett. Math. Phys. 43 (1998) 105 MR1607296
16	X Liu, Quantum Teichmüller space as a noncommutative algebraic object (2004) arXiv:math.GT/0408361
17	S Montgomery, Hopf algebras and their actions on rings, CBMS Regional Conference Series in Mathematics 82, Published for the Conference Board of the Mathematical Sciences, Washington, DC (1993) MR1243637
18	H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85 MR1828373
19	H Murakami, J Murakami, M Okamoto, T Takata, Y Yokota, Kashaev's conjecture and the Chern–Simons invariants of knots and links, Experiment. Math. 11 (2002) 427 MR1959752
20	N Reshetikhin, V G Turaev, Invariants of 3–manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547 MR1091619