Orbits and their accumulation points of cyclic subgroups of modular groups
type: Item
instance of: scholarly article
title: Orbits and their accumulation points of cyclic subgroups of modular groups
zbMATH Open document ID: 0744.30035
author: Harumi Tanigawa
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1992-06-26T00:00:00Z
review text: The author discusses the geometry of elements of the Teichmüller group for Riemann surfaces of signature \((g,p)\). These can be classified as elliptic, parabolic, hyperbolic and pseudo-hyperbolic. She gives an elegant proof of an assertion of Bers that an invariant line of a hyperbolic element is unique. She also gives a new proof of an unpublished theorem of McCarthy which asserts that if \(\gamma_ 1\) is hyperbolic and if \(\gamma_ 2\) normalizes the cyclic group generated by \(\gamma_ 1\) then \(\gamma_ 2\gamma_ 1\gamma_ 2^{-1}=\gamma_ 1^{\pm1}\) and describes the possible \(\gamma_ 2\) more precisely. Finally she gives some further applications of the same techniques.
reviewed by: Samuel James Patterson
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 20410
zbMATH Keywords: Teichmüller group
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: cyclic group
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227499
OpenAlex ID: W2026664729
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DOI: 10.2748/TMJ/1178227499
description: scientific article; zbMATH DE number 20410