Realizations of self branched coverings of the 2-sphere

Abstract : For a degree d self branched covering of the 2-sphere, a notable combinatorial invariant is an integer partition of 2d − 2, consisting of the multiplicities of the critical points. A finer invariant is the so called Hurwitz passport. The realization problem of Hurwitz passports remain largely open till today. In this article, we introduce two different types of finer invariants: a bipartite map and an incident matrix. We then settle completely their realization problem by showing that a map, or a matrix, is realized by a branched covering if and only if it satisfies a certain balanced condition. A variant of the bipartite map approach was initiated by W. Thurston. Our results shed some new lights to the Hurwitz passport problem.
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Contributeur : Jérôme Tomasini <>
Soumis le : vendredi 3 avril 2015 - 22:04:49
Dernière modification le : lundi 5 février 2018 - 15:00:03
Document(s) archivé(s) le : samedi 4 juillet 2015 - 10:27:22


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  • HAL Id : hal-01139321, version 1
  • ARXIV : 1504.01154



J Tomasini. Realizations of self branched coverings of the 2-sphere. 2015. 〈hal-01139321〉



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