Liouville central charge in quantum Teichmuller theory

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In the quantum Teichmuller theory, based on Penner coordinates, the mapping class groups of punctured surfaces are represented projectively. The case of a genus three surface with one puncture is worked out explicitly. The projective factor is calculated. It is given by the exponential of the Liouville central charge.
11 pages, 8 built in figures, latex2e

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