Geodesic
A quantum Teichm\"uller space
Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 3, pp. 511-528

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We explicitly describe a noncommutative deformation of the $*$-algebra of functions on the Teichmüller space of Riemann surfaces with holes that is equivariant with respect to the action of the mapping class group. 
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     author = {V. V. Fock and L. O. Chekhov},
     title = {A quantum {Teichm\"uller} space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {511--528},
     publisher = {mathdoc},
     volume = {120},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_120_3_a10/}
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V. V. Fock; L. O. Chekhov. A quantum Teichm\"uller space. Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 3, pp. 511-528. http://geodesic.mathdoc.fr/item/TMF_1999_120_3_a10/