Realization of primitive branched coverings over closed surfaces following the Hurwitz approach
type: Item
instance of: scholarly article
title: Realization of primitive branched coverings over closed surfaces following the Hurwitz approach
zbMATH Open document ID: 1039.57001
DOI: 10.2478/BF02476007
author: Heiner Zieschang
author: S. A. Bogatyi
author: Daciberg Lima Gonçalves
author: E. A. Kudryavtseva
published in: Central European Journal of Mathematics
publication date: 2004-01-27T00:00:00Z
review text: This paper studies the existence and classification of connected branched coverings of a closed surface. The approach taken here is purely algebraic following the ideas of Hurwitz. Specifically, let \(V\) be a closed surface, \(H\subset\pi_1(V)\) a subgroup of finite index and \(\{A_1,\dots, A_m\}\) a collection of partitions of an integer \(d\geq 2\). One wants conditions under which there is a connected branched covering \(f: W\to V\) of order \(d\) with branch data the given partitions and having \(f_{\#}\pi_1(W)= H\). Then one wishes to know how many different such coverings there are.
Mathematics Subject Classification ID: 57M12
zbMATH DE Number: 1978731
zbMATH Keywords: covering
zbMATH Keywords: branched covering of surfaces
zbMATH Keywords: branching order
zbMATH Keywords: Hurwitz problem
zbMATH Keywords: representations of the symmetry group \(\Sigma_d\)
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1978731