Quantum traces for representations of surface groups in SL_2

Details Quantum traces for representations of surface groups in SL_2 Quantum traces for representations of surface groups in SL_2

2010-03-27

arxiv.org/abs/1003.5250v4

Mathematics

Geometric Topology

40 pages, 25 figures. Version 2: Fixed classical case. Misprints corrected. Version 3: More misprints corrected, including sta

Scientific paper

We consider two different quantizations of the character variety consisting of all representations of surface groups in SL_2. One is the skein algebra considered by Przytycki-Sikora and Turaev. The other is the quantum Teichmuller space introduced by Chekhov-Fock and Kashaev. We construct a homomorphism from the skein algebra to the quantum Teichmuller space which, when restricted the classical case, corresponds to the equivalence between these two algebras through trace functions.

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