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arXiv · 1003.5250

Quantum traces for representations of surface groups in SL_2

Francis Bonahon·Helen Wong
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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.

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Francis Bonahon, Helen Wong. 2010-12-17. Quantum traces for representations of surface groups in SL_2. https://doi.org/10.2140/gt.2011.15.1569

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