A Uniqueness Property for the Quantization of Teichmüller Spaces

2005/09/28 by Hua Bai, Bai, Hua
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Geometric and Algebraic Topology #math.GT #math.QA #msc:20G42 #msc:57M50 #msc:57R56

paper · pdf · doi:10.48550/arxiv.math/0509679

14 pages, 3 figures

arxiv created 2005/09/28 · arxiv updated 2009/12/01

Abstract

Chekhov, Fock and Kashaev introduced a quantization of the Teichmüller space T^q(S) of a punctured surface S, and an exponential version of this construction was developed by Bonahon and Liu. The construction of the quantum Teichmüller space crucially depends on certain coordinate change isomorphisms between the Chekhov-Fock algebras associated to different ideal triangulations of S. We show that these coordinate change isomorphisms are essentially unique, once we require them to satisfy a certain number of natural conditions.

Related

• The quantum Teichmuller space as a noncommutative algebraic object
• Local representations of the quantum Teichmuller space
• Quantization of Teichmüller spaces and the quantum dilogarithm
• Intertwining operators of the quantum Teichmüller space
• Quantum Teichmüller space