Homology coverings of Riemann surfaces
type: Item
instance of: scholarly article
title: Homology coverings of Riemann surfaces
zbMATH Open document ID: 0787.30029
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1994-04-12T00:00:00Z
review text: We extend a result on homology coverings of closed Riemann surfaces due to Maskit to the class of analytically finite ones. We show that if \(S\) is an analytically finite hyperbolic Riemann surface, then its conformal structure is determined by the conformal structure of its homology cover. The homology cover of a Riemann surface \(S\) is the highest regular covering of \(S\) with an Abelian group of covering transformations. In fact, we show that the commutator subgroup of any torsion-free, finitely generated Fuchsian group of the first kind determines it uniquely.
Mathematics Subject Classification ID: 30F20
Mathematics Subject Classification ID: 30F45
zbMATH DE Number: 549621
zbMATH Keywords: analytically finite Riemann surfaces
zbMATH Keywords: homology coverings
author: Rubén A. Hidalgo
reviewed by: Rubén A. Hidalgo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225844
OpenAlex ID: W1977897424
cites work: The homology covering of a Riemann surface
DOI: 10.2748/TMJ/1178225844
description: scientific article; zbMATH DE number 549621