Volume 15, issue 3 (2011)

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

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

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 Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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