Global real analytic length parameters for Teichmüller spaces
type: Item
instance of: scholarly article
title: Global real analytic length parameters for Teichmüller spaces
zbMATH Open document ID: 0858.32016
author: Yoshihide Okumura
published in: Hiroshima Mathematical Journal
publication date: 1996-07-07T00:00:00Z
review text: The Teichmüller space, \(T(g)\), comprising conjugacy classes of marked Fuchsian groups of type \((g,0,0)\), is a bounded complex analytic manifold of complex dimension \(3g-3\), for each genus \(g \geq 2\). In this paper an explicit description of \(T(2)\) as a real analytic manifold is shown, utilizing seven ``length parameters'' (which are the absolute value of traces of certain chosen elements in the varying Fuchsian groups). The seven parameters (and it is known that six will not suffice for a global parametrization), are related by one algebraic relationship, and are subject to certain simple inequalities. The author claims that a similar result is possible, by induction, for a real analytic description of \(T(g)\), \(g\geq 3\) using \(6g-5\) length parameters. That is not shown in this article. One difficulty in reading the present paper is that some calculations rely on results quoted by the author from another manuscript [`Geometry of Möbius transformations acting on the hyperbolic plane and characterization of simple dividing loops on Riemann surfaces'] which is asserted to be ``in preparation''.
reviewed by: Subhashis Nag
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 30F35
zbMATH DE Number: 897340
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: Teichmüller space
zbMATH Keywords: Fuchsian groups
zbMATH Keywords: length parameters
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 897340