Maps on surfaces and Galois groups (Q2702744)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maps on surfaces and Galois groups |
scientific article |
Statements
13 March 2001
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surface
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Riemann surface
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algebraic curve
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Galois group
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bipartite graph
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Maps on surfaces and Galois groups (English)
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Inspired by a theorem of \textit{G. V. Belyj} [Izv. Akad. Nauk SSSR, Ser. Mat. 43, No. 2, 267-276, 479 (1979; Zbl 0409.12012)], \textit{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.
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