Geodesic
Liouville Central Charge in Quantum Teichm\"uller Theory
Informatics and Automation, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 72-81.

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In the quantum Teichmüller 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 analyzed explicitly. The projective factor is calculated. It is given by the exponential of the Liouville central charge. 
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R. M. Kashaev. Liouville Central Charge in Quantum Teichm\"uller Theory. Informatics and Automation, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 72-81. http://geodesic.mathdoc.fr/item/TRSPY_1999_226_a5/

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