Plane trees and classical mathematics
During the Montpellier period of his work (1970-1984), \textit{Alexander Grothendieck} raised a new wave of interest in visualizable objects in the mathematical community. He introduced ``dessins d'enfants'', a class of graphs on oriented surfaces. Mathematically dessins were by no means new -- versions of them called maps, fatgraphs, ribbon graphs, etc. had already been introduced and studied by various authors. However, psychologically they were new, at least from the point of view that they were related to various branches of mathematics and physics. A. Grothendieck was fascinated by the relations between dessins d'enfants and arithmetical geometry. He summarized his ideas in the paper ``Esquisse d'un programme'', which is now published [see \textit{A. Grothendieck}, in: Proc. Conf. Geometry Arithmetic of Moduli spaces, Luminy 1995, Lond. Math, Soc. Lect. Note Ser. 242, 5-48 (1997; Zbl 0901.14001)], and since then the constructions of this paper have gradually started to find a place of their own in such domains of modern activities as inverse Galois theory, quantum gravity, etc. The goal of the present paper is to demonstrate that dessins d'enfants are also closely related to classical mathematics. This work is addressed to the general mathematical community and does not presuppose any preliminary special knowledge.
scientific article; zbMATH DE number 1017596