Quantization of Teichmüller spaces and the quantum dilogarithm

Details Quantization of Teichmüller spaces and the quantum dilogarithm Quantization of Teichmüller spaces and the quantum dilogarithm

1997-05-27

arxiv.org/abs/q-alg/9705021v1

Mathematics

Quantum Algebra

Latex2e, 11 pages with 4 figures

Scientific paper

The Teichm\"uller 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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