Volume 15, issue 3 (2011)

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

Volume 29, 1 issue

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Quantum traces for representations of surface groups in $\mathrm{SL}_2(\mathbb{C})$

Francis Bonahon and Helen Wong

Geometry & Topology 15 (2011) 1569–1615
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 J W Barrett, Skein spaces and spin structures, Math. Proc. Cambridge Philos. Soc. 126 (1999) 267 MR1670233
4 F Bonahon, Low-dimensional geometry: From Euclidean surfaces to hyperbolic knots, Student Math. Library, IAS/Park City Mathematical Subseries 49, Amer. Math. Soc. (2009) MR2522946
5 F Bonahon, X Liu, Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms, Geom. Topol. 11 (2007) 889 MR2326938
6 F Bonahon, H Wong, Kauffman brackets, character varieties and triangulations of surfaces, from: "Proceedings of the Conference on Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric structures held in honor of Wiliam Jaco's 70th birthday on June 4–6, 2010 at Oklahoma State University in Stillwater, OK" (editors L Bartolini, D Gabai, J Johnson, W Li, F Luo, R Myers, H Rubinstein), to appear in Contemporary Math., Amer. Math. Soc.
7 F Bonahon, H Wong, Representations of the Kauffman skein algebra I: Punctured surfaces, in preparation
8 F Bonahon, H Wong, Representations of the Kauffman skein algebra II: Closed surfaces and naturality, in preparation
9 D Bullock, Estimating a skein module with $\mathrm{SL}_2({\C})$ characters, Proc. Amer. Math. Soc. 125 (1997) 1835 MR1403115
10 D Bullock, Rings of $\mathrm{SL}_2({\C})$–characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997) 521 MR1600138
11 D Bullock, C Frohman, J Kania-Bartoszyńska, Topological interpretations of lattice gauge field theory, Comm. Math. Phys. 198 (1998) 47 MR1657365
12 D Bullock, C Frohman, J Kania-Bartoszyńska, Understanding the Kauffman bracket skein module, J. Knot Theory Ramifications 8 (1999) 265 MR1691437
13 D Bullock, C Frohman, J Kania-Bartoszyńska, The Kauffman bracket skein as an algebra of observables, Proc. Amer. Math. Soc. 130 (2002) 2479 MR1897475
14 L O Chekhov, V V Fock, Quantum Teichmüller spaces, Teoret. Mat. Fiz. 120 (1999) 511 MR1737362
15 L O Chekhov, V V Fock, Observables in 3D gravity and geodesic algebras, from: "Quantum groups and integrable systems (Prague, 2000)" (editor Č Burdík), Czechoslovak J. Phys. 50, Academy of Sci. of the Czech Republic Inst. of Physics (2000) 1201 MR1806262
16 L O Chekhov, R C Penner, Introduction to Thurston's quantum theory, Uspekhi Mat. Nauk 58 (2003) 93 MR2054091
17 P M Cohn, Skew fields: Theory of general division rings, Encyclopedia of Math. and its Appl. 57, Cambridge Univ. Press (1995) MR1349108
18 V V Fock, Dual Teichmüller spaces arXiv:dg-ga/9702018
19 W M Goldman, The symplectic nature of fundamental groups of surfaces, Adv. in Math. 54 (1984) 200 MR762512
20 W M Goldman, Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math. 85 (1986) 263 MR846929
21 R Guo, X Liu, Quantum Teichmüller space and Kashaev algebra, Algebr. Geom. Topol. 9 (2009) 1791 MR2550095
22 J L Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math. 84 (1986) 157 MR830043
23 H Helling, Diskrete Untergruppen von $\mathrm{SL}_{2}({\R})$, Invent. Math. 17 (1972) 217 MR0324075
24 C Hiatt, Quantum traces in quantum Teichmüller theory, Algebr. Geom. Topol. 10 (2010) 1245 MR2661526
25 R M Kashaev, Quantization of Teichmüller spaces and the quantum dilogarithm, Lett. Math. Phys. 43 (1998) 105 MR1607296
26 C Kassel, Quantum groups, Graduate Texts in Math. 155, Springer (1995) MR1321145
27 W B R Lickorish, An introduction to knot theory, Graduate Texts in Math. 175, Springer (1997) MR1472978
28 X Liu, The quantum Teichmüller space as a noncommutative algebraic object, J. Knot Theory Ramifications 18 (2009) 705 MR2527682
29 D Mumford, J Fogarty, F Kirwan, Geometric invariant theory, Ergebnisse der Math. und ihrer Grenzgebiete (2) 34, Springer (1994) MR1304906
30 R C Penner, The decorated Teichmüller space of punctured surfaces, Comm. Math. Phys. 113 (1987) 299 MR919235
31 H Petersson, Über eine Metrisierung der automorphen Formen und die Theorie der Poincaréschen Reihen, Math. Ann. 117 (1940) 453 MR0002624
32 J H Przytycki, A S Sikora, On skein algebras and $\mathrm{SL}_2({\C})$–character varieties, Topology 39 (2000) 115 MR1710996
33 W P Thurston, Minimal stretch maps between hyperbolic surfaces arXiv:math/9801039
34 W P Thurston, Three-dimensional geometry and topology. Vol. 1, (S Levy, editor), Princeton Math. Series 35, Princeton Univ. Press (1997) MR1435975
35 V G Turaev, Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. $(4)$ 24 (1991) 635 MR1142906
36 A Weil, Modules des surfaces de Riemann, from: "Scientific works, Collected papers, Vol. II (1951–1964)", Springer (1979) 381 MR537935