A topological property of Teichmüller spaces
type: Item
instance of: scholarly article
title: A topological property of Teichmüller spaces
zbMATH Open document ID: 0595.32030
DOI: 10.1007/BF01158405
author: I. V. Zhuravlev
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: A subset A in a topological space X is called an open domain if it is the interior of its closure. In this paper it is shown that the Teichmüller space of an arbitrary Fuchsian group is an open domain in the set of bounded holomorphic quadratic differentials for that group. Bounded means in the Bers norm. The result follows easily from a previous result of the author [Sov. Math., Dokl. 21, 252-255 (1980); translation from Dokl. Akad. Nauk SSSR, 250, 1047-1050 (1980; Zbl 0467.30037)]. The theorem has also been proved by Bers and generalizes a result of the reviewer valid only for finite dimensional Teichmüller spaces [Ann. Math. Stud. 97, 3- 5 (1981; Zbl 0458.30031)].
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 30F30
zbMATH DE Number: 3957619
zbMATH Keywords: Bers imbedding
zbMATH Keywords: Teichmüller space
zbMATH Keywords: Fuchsian group
zbMATH Keywords: bounded holomorphic quadratic differentials
MaRDI profile type: Publication
cites work: Q3907818
cites work: Q3919950
full work available at URL: https://doi.org/10.1007/bf01158405
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description: scientific article; zbMATH DE number 3957619