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Quantum traces for
representations of surface groups in
$\mathrm{SL}_2(\mathbb{C})$
Francis Bonahon and Helen Wong |
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Geometry & Topology 15 (2011) 1569–1615
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Abstract |
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We relate two different quantizations of the character variety consisting of all representations of surface groups in . One is the Kauffman skein algebra considered by Bullock, Frohman and Kania-Bartoszyńska, Przytycki and Sikora, and Turaev. The other is the quantum Teichmüller space introduced by Chekhov and Fock and by Kashaev. We construct a homomorphism from the skein algebra to the quantum Teichmüller space which, when restricted to the classical case, corresponds to the equivalence between these two algebras through trace functions. |
Keywords
Kauffman skein relation, character variety, surface group,
skein module, skein algebra, quantum Teichmüller theory
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Mathematical Subject Classification 2010
Primary: 14D20, 57M25, 57R56
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References |
Publication
Received: 10 January 2011
Revised: 10 January 2011
Accepted: 18 July 2011
Published: 19 September 2011
Proposed: Walter Neumann
Seconded: Jean-Pierre Otal, David Gabai
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Authors |
| Francis Bonahon | |
| Department of Mathematics University of Southern California 3620 S Vermont Ave, KAP 108 Los Angeles CA 90089-2532 USA |
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| http://www-rcf.usc.edu/~fbonahon/ | |
| Helen Wong | |
| Department of Mathematics Carleton College 1 North College St Northfield MN 55057 USA |
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| http://people.carleton.edu/~hwong | |
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