The equivariant fundamental group, uniformization of real algebraic curves, and global complex analytic coordinates on Teichmüller spaces.
type: Item
instance of: scholarly article
title: The equivariant fundamental group, uniformization of real algebraic curves, and global complex analytic coordinates on Teichmüller spaces.
zbMATH Open document ID: 1054.30042
author: Johannes Huisman
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2001-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73562
review text: The author constructs explicitly an Earle's slice by using a co-compact torsion free Fuchsian group \(\Gamma\), acting on the upper-half plane \(\mathbb H\), so that there is an anticonformal automorphism \(\tau:{\mathbb H} \to {\mathbb H}\) satisfying \(\tau^{2} \in \Gamma\) and \(\tau \Gamma \tau^{-1} = \Gamma\). In this way, he obtains a global complex parameter for the Teichmüller space of \(\Gamma\) which restricts to a global real paramater for \(\langle \Gamma, \tau \rangle\), that is, for the (real) Teichmüller space of real algebraic curves.
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 30F50
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 14H15
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 1911462
zbMATH Keywords: real algebraic curves
zbMATH Keywords: Teichmüller spaces
zbMATH Keywords: Kleinian groups
reviewed by: Rubén A. Hidalgo
MaRDI profile type: Publication
OpenAlex ID: W2330143058
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DOI: 10.5802/AFST.1007
description: scientific article; zbMATH DE number 1911462