Number of nonequivalent coverings over a nonorientable compact surface
type: Item
instance of: scholarly article
title: Number of nonequivalent coverings over a nonorientable compact surface
zbMATH Open document ID: 0598.30059
DOI: 10.1007/BF00969347
author: G. G. Pozdnyakova
author: Alexander Mednykh
published in: Siberian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Let S be a compact surface and \(\pi\) : \(T\to S\) and \(\pi\) ': T'\(\to S\) two coverings over S. We say that \(\pi\) and \(\pi\) ' are equivalent if there exists a homeomorphism \(h: T\to T'\) such that \(\pi =\pi '\circ h\). The first author [Sib. Mat. Zh. 23, No.3, 155-160 (1982; Zbl 0513.30036)] had obtained the exact formulas for the number of non-equivalent coverings over orientable surface S having a given multiplicity. This result can be considered as a partial solution of the Hurwitz enumeration problem completely solved by the same author [Sib. Mat. Zh. 25, No.4(146), 120-142 (1984; reviewed above)]. In the present paper the number of subgroups of a given index in the fundamental group of non-orientable surface S are determined and the number of non-equivalent coverings over S of a given multiplicity are obtained.
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 3964350
zbMATH Keywords: coverings
MaRDI profile type: Publication
cites work: Hurwitz problem on the number of nonequivalent coverings of a compact Riemann surface
cites work: Über einen Satz von Dey und die Modulgruppe
cites work: Automorphisms of compact non-orientable Riemann surfaces
cites work: Q3253828
cites work: Branch Point Structure of Covering Maps Onto Nonorientable Surfaces
cites work: Q5631018
description: scientific article; zbMATH DE number 3964350