Quantum traces for representations of surface groups in SL_2
Geometric Topology
2018-08-02 v4 Quantum Algebra
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.
Cite
@article{arxiv.1003.5250,
title = {Quantum traces for representations of surface groups in SL_2},
author = {Francis Bonahon and Helen Wong},
journal= {arXiv preprint arXiv:1003.5250},
year = {2018}
}
Comments
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