Parametrization of Möbius groups acting in a disk
type: Item
instance of: scholarly article
title: Parametrization of Möbius groups acting in a disk
zbMATH Open document ID: 0606.30042
DOI: 10.1007/BF02621907
author: Tuomas Sorvali
author: Mika Seppälä
published in: Commentarii Mathematici Helvetici
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140045
review text: We parametrize groups of Möbius-transformations by multipliers of the elements of the group. Let G be a group generated by 2g, \(g>1\), hyperbolic Möbius-transformations mapping the upper half-plane U onto itself. Supposing that the set of generators of G satisfies one relation and certain technical conditions we construct a set of 6g-4 elements of G such that the multipliers of these Möbius-transformations parametrize G up to conjugation by a Möbius-transformation. The group G need not be discontinuous. In the case of a Fuchsian group G we can apply these considerations to get a parametrization for the Teichmüller space of compact genus g Riemann surfaces by 6g-4 geodesic length functions.
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 14H15
zbMATH DE Number: 3979484
zbMATH Keywords: Möbius groups
zbMATH Keywords: parametrization
zbMATH Keywords: geodesic length functions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3979484