The Chekhov--Fock parametrization of Teichm\"uller 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.
@article{FPM_2007_13_6_a12,
author = {G. B. Shabat and V. I. Zolotarskaya},
title = {The {Chekhov--Fock} parametrization of {Teichm\"uller} spaces and dessins d'enfants},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {217--226},
publisher = {mathdoc},
volume = {13},
number = {6},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a12/}
}
TY - JOUR AU - G. B. Shabat AU - V. I. Zolotarskaya TI - The Chekhov--Fock parametrization of Teichm\"uller spaces and dessins d'enfants JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2007 SP - 217 EP - 226 VL - 13 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a12/ LA - ru ID - FPM_2007_13_6_a12 ER -
%0 Journal Article %A G. B. Shabat %A V. I. Zolotarskaya %T The Chekhov--Fock parametrization of Teichm\"uller spaces and dessins d'enfants %J Fundamentalʹnaâ i prikladnaâ matematika %D 2007 %P 217-226 %V 13 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a12/ %G ru %F FPM_2007_13_6_a12
G. B. Shabat; V. I. Zolotarskaya. The Chekhov--Fock parametrization of Teichm\"uller 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/