Quantum traces for representations of surface groups in SL_2

Abstract

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.

40 pages, 25 figures. Version 2: Fixed classical case. Misprints corrected. Version 3: More misprints corrected, including statement of Lemma 22. Added observation that the quantum trace homomorphism is injective. Version 4: Final corrections before submission

References in corpus (1)

• Quantum Teichmüller space and Kashaev algebra

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