The order of periodic elements of Teichmüller modular groups
type: Item
instance of: scholarly article
title: The order of periodic elements of Teichmüller modular groups
zbMATH Open document ID: 1071.30041
author: Ege Fujikawa
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2005-07-01T00:00:00Z
review text: Let \(R\) be a Riemann surface with possibly an infinitely generated fundamental group. It is well-known that if \(f\) is a conformal automorphism of \(R\), then \(f\) has finite order and the corresponding element in the mapping class group of \(f\) fixes a point in the Teichmüller space of \(R\). In a previous paper, the author obtained an upper bound for the order of \(f\) in terms of the injectivity radius of \(R\). In the paper under review, the author obtains an extension to the case where \(f\) is quasi-conformal. He shows that in the case where \(f\) fixes the homotopy class of a nontrivial simple closed curve, if the maximal dilatation of \(f\) is smaller than some constant depending on the injectivity radius of \(R\), then the corresponding mapping class is periodic, and he obtains an estimate on the order of the period.
reviewed by: Athanase Papadopoulos
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 2185490
zbMATH Keywords: Teichmüller modular group
zbMATH Keywords: Teichmueller space
zbMATH Keywords: conformal automorphism
zbMATH Keywords: quasiconformal automorphism
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1113234833
OpenAlex ID: W2065391221
cites work: Q4517812
cites work: Q3310101
cites work: The order of conformal automorphisms of Riemannian surfaces of infinite type
cites work: Q4662429
cites work: On the action of the mapping class group for Riemann surfaces of infinite type
cites work: On Marden's universal constant of Fuchsian groups. II
DOI: 10.2748/TMJ/1113234833
description: scientific article; zbMATH DE number 2185490