Plane trees and classical mathematics
type: Item
instance of: scholarly article
title: Plane trees and classical mathematics
zbMATH Open document ID: 0901.14017
DOI: 10.1007/BF02362630
published in: Journal of Mathematical Sciences (New York)
publication date: 1997-11-06T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14N10
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 33B10
zbMATH DE Number: 1017596
zbMATH Keywords: dessins d'enfants
zbMATH Keywords: inverse Galois theory
author: Nikolai Adrianov
author: George Shabat
MaRDI profile type: Publication
cites work: Composition of plane trees
cites work: Q4364755
cites work: Q5821083
cites work: Q4320820
Wikidata QID: Q125974324
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description: scientific article; zbMATH DE number 1017596