Geodesic
The Chekhov–Fock parametrization of Teichmüller spaces and dessins d'enfants
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 6, pp. 217-226
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The construction of Chekhov and Fock, which associates a complex structure to a trivalent ribbon graph with real numbers on its edges, is reformulated in cartographic terms. It turns out that the “dessins d'enfants” construction corresponds to zero numbers. Two examples are discussed, and the future development of the theory is suggested. 
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G. B. Shabat; V. I. Zolotarskaya. The Chekhov–Fock parametrization of Teichmüller spaces and dessins d'enfants. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 6, pp. 217-226. http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a12/

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