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Calculating and Drawing Belyi Pairs

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The paper contains a survey of the current state of a constructive part in dessin d’enfants theory. Namely, it is devoted to actual establishing the correspondence between the Belyi pairs and their combinatorial-topological representations. This correspondence is established in terms of equivalence of categories, and all relevant categories are introduced. Several connections with arithmetic are discussed. One of the sections presents a possible generalization of the theory, in which three branch points, allowed for the Belyi functions, are replaced by four. Several directions for further research are presented. Bibliography: 80 titles.

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  1. Russian State University for the Humanities, Moscow, Russia

    G. Shabat

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 446, 2016, pp. 182–220.

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Shabat, G. Calculating and Drawing Belyi Pairs. J Math Sci 226, 667–693 (2017). https://doi.org/10.1007/s10958-017-3557-3

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