On the Chekhov-Fock coordinates of "dessins d'enfants".
by
Vera Zolotarskaia
Moscow State University

There are several ways to associate a complex structure to a ribbon graph (see [2], [3], [4]). In the construction of dessins d'enfants[4] a single riemann surface is associated to each graph. We call it the Grothendieck model of a ribbon graph. The goal of the present paper is to discuss one more such construction, depending on some parameters - that of Chekhov-Fock [1]. We prove that putting all parametres equal to 0, we obtain the Grothendieck model of this graph.

[1] V.V.Fock and L.O. Chekhov, "Quantim Mapping Class Group, Pentagon Relation and Geodesics", Proceedings of the Steklov Institute of Mathematics, Vol. 226, 1999, pp. 149-163.

[2] Kontsevich M.L. "Intersection theory on the moduli space of curves", functional analysis and it's applications, 1991, 25:2 pp. 50-57, in russian.

[3] Penner R.C. "The decorated Teichmuller Space of punctured surfaces", Comm. Math. Phys., 113:2 (1987), 299-340.

[4] Shabat G.B. "Combinatorial and topological methods in the theory of algebraic curves", Theses, Moscow State University, 1998, in russian.

Date received: November 27, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cake-03.