A Uniqueness Property for the Quantization of Teichmüller Spaces

Details A Uniqueness Property for the Quantization of Teichmüller Spaces A Uniqueness Property for the Quantization of Teichmüller Spaces

2005-09-28

arxiv.org/abs/math/0509679v1

Mathematics

Geometric Topology

14 pages, 3 figures

Scientific paper

Chekhov, Fock and Kashaev introduced a quantization of the Teichm\"{u}ller space $\mathcal{T}^q(S)$ of a punctured surface $S$, and an exponential version of this construction was developed by Bonahon and Liu. The construction of the quantum Teichm\"{u}ller 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.

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