Journal of the Mathematical Society of Japan

On the action of the mapping class group for Riemann surfaces of infinite type

Ege FUJIKAWA, Hiroshige SHIGA, and Masahiko TANIGUCHI

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Abstract

We consider Riemann surfaces of infinite type and their reduced Teichmüller spaces. The reduced Teichmüller space admits the action of the reduced mapping class group. Generally, the action is not discrete while it is faithful. We give sufficient conditions for the discreteness of the action in terms of the geometry of Riemann surfaces.

Article information

Source
J. Math. Soc. Japan Volume 56, Number 4 (2004), 1069-1086.

Dates
First available in Project Euclid: 27 September 2007

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1190905449

Digital Object Identifier
doi:10.2969/jmsj/1190905449

Mathematical Reviews number (MathSciNet)
MR2091417

Zentralblatt MATH identifier
1064.30047

Subjects
Primary: 30F60: Teichmüller theory [See also 32G15]
Secondary: 30C62: Quasiconformal mappings in the plane

Keywords
Teichmüller space mapping class group hyperbolic geometry

Citation

FUJIKAWA, Ege; SHIGA, Hiroshige; TANIGUCHI, Masahiko. On the action of the mapping class group for Riemann surfaces of infinite type. J. Math. Soc. Japan 56 (2004), no. 4, 1069--1086. doi:10.2969/jmsj/1190905449. http://projecteuclid.org/euclid.jmsj/1190905449.


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