Quantization of Teichmüller spaces and the quantum dilogarithm

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.

Latex2e, 11 pages with 4 figures

References in corpus (6)

• Discrete Heisenberg-Weyl Group and Modular Group
• Quantum Dilogarithm
• Combinatorial quantization of the Hamiltonian Chern-Simons theory I
• A Link Invariant from Quantum Dilogarithm
• Quantum Dilogarithm as a 6j-Symbol
• Link Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory

Cited by in corpus (6)

• The pentagon relation for the quantum dilogarithm and quantized M_{0,5}
• Lambda<0 Quantum Gravity in 2+1 Dimensions I: Quantum States and Stringy S-Matrix
• Dimer Models, Integrable Systems and Quantum Teichmuller Space
• Spectral problem on graphs and L-functions
• Heisenberg double and Drinfeld double of the quantum superplane
• Finite dimensional quantum Teichmüller space from the quantum torus at root of unity