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Fundamentalnaya i Prikladnaya Matematika, 2007, Volume 13, Issue 6, Pages 217–226 (Mi fpm1093)  
The Chekhov–Fock parametrization of Teichmüller spaces and dessins d'enfants

G. B. Shabata, V. I. Zolotarskayab

a Russian State University for the Humanities
b Deloitte
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Abstract: 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.
English version:
Journal of Mathematical Sciences (New York), 2009, Volume 158, Issue 1, Pages 155–161
DOI: https://doi.org/10.1007/s10958-009-9368-4
Bibliographic databases:
UDC: 512.7+515.162
Language: Russian
Citation: G. B. Shabat, V. I. Zolotarskaya, “The Chekhov–Fock parametrization of Teichmüller spaces and dessins d'enfants”, Fundam. Prikl. Mat., 13:6 (2007), 217–226; J. Math. Sci., 158:1 (2009), 155–161
Citation in format AMSBIB
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\by G.~B.~Shabat, V.~I.~Zolotarskaya
\paper The Chekhov--Fock parametrization of Teichm\"uller spaces and dessins d'enfants
\jour Fundam. Prikl. Mat.
\yr 2007
\vol 13
\issue 6
\pages 217--226
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2476037}
\elib{https://elibrary.ru/item.asp?id=11162705}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 158
\issue 1
\pages 155--161
\crossref{https://doi.org/10.1007/s10958-009-9368-4}
\elib{https://elibrary.ru/item.asp?id=13600728}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-62249142052}
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    		Фундаментальная и прикладная математика
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