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April, 2007 Teichmüller spaces for pointed Fuchsian groups and their modular groups
Yuliang SHEN
J. Math. Soc. Japan 59(2): 301-321 (April, 2007). DOI: 10.2969/jmsj/05920301


It is known that the modular group Mod X acts discontinuously (but not freely) on the Teichmüller space T ( X ) for a finite type Riemann surface X , while it does not necessarily act discontinuously on T ( X ) when X is of infinite type. The primary purpose of the paper is to discuss those subgroups of Mod X acting discontinuously and freely on T ( X ) and to discuss the properties of the corresponding quotient complex manifolds as well. Actually, we will discuss some generalized Teichmüller spaces, the Teichmüller spaces for pointed Riemann surfaces and pointed Fuchsian groups, and their modular groups, generalizing and completing some results of Bers [Be1], Kra [Kr1] and Nag ([Na1], [Na3], [Na4]).


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Yuliang SHEN. "Teichmüller spaces for pointed Fuchsian groups and their modular groups." J. Math. Soc. Japan 59 (2) 301 - 321, April, 2007.


Published: April, 2007
First available in Project Euclid: 1 October 2007

zbMATH: 1119.30025
MathSciNet: MR2325687
Digital Object Identifier: 10.2969/jmsj/05920301

Primary: 32G15
Secondary: 30C60 , 30F60

Keywords: biholomorphic isomorphism , Fuchsian group , modular group , Riemann surface , Teichmüller space

Rights: Copyright © 2007 Mathematical Society of Japan


Vol.59 • No. 2 • April, 2007
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