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Dessins d’enfants: bipartite maps and Galois groups. (English) Zbl 0970.14018

Summary: Belyi’s theorem implies that the Riemann surfaces defined over the field of algebraic numbers are precisely those which support bipartite maps; this provides a faithful representation of the Galois group of this field on these combinatorial objects.

MSC:

14H55 Riemann surfaces; Weierstrass points; gap sequences
05B99 Designs and configurations
12F12 Inverse Galois theory
14H25 Arithmetic ground fields for curves
11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields
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