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Maps on surfaces and Galois groups. (English) Zbl 0958.05036
Inspired by a theorem of G. V. Belyj [Izv. Akad. Nauk SSSR, Ser. Mat. 43, No. 2, 267-276, 479 (1979; Zbl 0409.12012)], A. Grothendieck [in Geometric Galois actions, Lond. Math. Soc. Lect. Notes Ser. 242, 5-48; English translation: 243-283 (1997; Zbl 0901.14001)] proposed a theory that Galois groups of algebraic number fields have faithful representations on maps on surfaces, called dessins d’enfants. The present author surveys some of the connections between maps on surfaces (particularly those involving bipartite graphs), permutations, Riemann surfaces, algebraic curves, and Galois groups.

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
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