Geometry & Topology 15 (2011) 1569–1615

DOI: 10.2140/gt.2011.15.1569

Abstract

We relate two different quantizations of the character variety consisting of all representations of surface groups in SL₂. One is the Kauffman skein algebra considered by Bullock, Frohman and Kania-Bartoszyńska, Przytycki and Sikora, and Turaev. The other is the quantum Teichmüller space introduced by Chekhov and Fock and by Kashaev. We construct a homomorphism from the skein algebra to the quantum Teichmüller space which, when restricted to the classical case, corresponds to the equivalence between these two algebras through trace functions.

Keywords

Kauffman skein relation, character variety, surface group, skein module, skein algebra, quantum Teichmüller theory

Mathematical Subject Classification

Primary: 14D20, 57M25, 57R56

References

Publication

Received: 10 January 2011
Revised: 10 January 2011
Accepted: 18 July 2011
Published: 19 September 2011
Proposed: Walter Neumann
Seconded: Jean-Pierre Otal, David Gabai

Authors