Quantum traces for representations of surface groups in SL2(ℂ)

By Francis Bonahon, Helen M. Wong. 2010

129 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8028626d564aca4c50c503e1480d2841ad560993

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In Geometry and Topology

1. J. Kania-Bartoszynska
2. Thang T. Q. Lê
3. C. Frohman
4. Adam S. Sikora
5. Józef H. Przytycki
6. Francesco Costantino
7. Helen M. Wong
8. Francis Bonahon

In Mathematical Physics

1. Thang T. Q. Lê
2. Adam S. Sikora
3. Józef H. Przytycki
4. Francesco Costantino
5. Helen M. Wong
6. Francis Bonahon

Citations in the corpus

• Unicity for representations of the Kauffman bracket skein algebra (2017, background): “For the case when F has at least one punctures and is triangulable (see below), this fact follows from the existence of the quantum trace map [5] which embeds Kζ (F) into a quantum torus which does not have non-trivial zero-divisors.”