FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 6, PAGES 217-226

The Chekhov--Fock parametrization of Teichmüller spaces and dessins d'enfants

G. B. Shabat
V. I. Zolotarskaia

Abstract

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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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Last modified: April 22, 2008