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Abstract : We consider the usual model of hypermaps or, equivalently, bipartite maps, represented by pairs of permutations that act transitively on a set of edges E. The specific feature of our construction is the fact that the elements of E are themselves or are labelled by rather complicated combinatorial objects, namely, the 4-constellations, while the permutations defining the hypermap originate from an action of the Hurwitz braid group on these 4-constellations.The motivation for the whole construction is the combinatorial representation of the parameter space of the ramified coverings of the Riemann sphere having four ramification points.

Keywords : Riemann surface ramified covering dessins d-enfants Belyi function braid group Hurwitz scheme





Author: Alexander Zvonkin -

Source: https://hal.archives-ouvertes.fr/



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