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.

Location: http://mech.math.msu.su/~fpm/eng/k07/k076/k07612h.htm

Last modified: April 22, 2008