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Quantization of Teichmüller Spaces and the Quantum Dilogarithm

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Abstract

The Teichmüller space of punctured surfaces with the Weil–Petersson symplectic structure and the action of the mapping class group is realized as the Hamiltonian reduction of a finite-dimensional symplectic space where the mapping class group acts by symplectic rational transformations. Upon quantization, the corresponding (projective) representation of the mapping class group is generated by the quantum dilogarithms.

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  1. Helsinki Institute of Physics, University of Helsinki, Helsinki, PO Box 9 (, Siltavuorenpenger 20 C), FIN-00014, Finland, e-mail

    R. M. Kashaev

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  1. R. M. Kashaev
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Kashaev, R.M. Quantization of Teichmüller Spaces and the Quantum Dilogarithm. Letters in Mathematical Physics 43, 105–115 (1998). https://doi.org/10.1023/A:1007460128279

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