Quantization of Teichmüller spaces and the quantum dilogarithm

1997/05/27 by Rinat Kashaev, Kashaev, R. M. · 4 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.q-alg/9705021

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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• Two Decades of Probabilistic Approach to Liouville Conformal Field Theory
• The pentagon relation for the quantum dilogarithm and quantized M_0,5
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• Heisenberg double and Drinfeld double of the quantum superplane

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