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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Pure mapping class group acting on Teichmüller space
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by Ege Fujikawa
Conform. Geom. Dyn. 12 (2008), 227-239
Published electronically: December 23, 2008


For a Riemann surface of analytically infinite type, the action of the quasiconformal mapping class group on the Teichmüller space is not discontinuous in general. In this paper, we consider pure mapping classes that fix all topological ends of a Riemann surface and prove that the pure mapping class group acts on the Teichmüller space discontinuously under a certain geometric condition of a Riemann surface. We also consider the action of the quasiconformal mapping class group on the asymptotic Teichmüller space. Non-trivial mapping classes can act on the asymptotic Teichmüller space trivially. We prove that all such mapping classes are contained in the pure mapping class group.
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Bibliographic Information
  • Ege Fujikawa
  • Affiliation: Department of Mathematics, Chiba University, 1-33 Yayoi-cho, Inage, Chiba, 263-8522, Japan
  • MR Author ID: 706593
  • Email:
  • Received by editor(s): May 19, 2008
  • Published electronically: December 23, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 12 (2008), 227-239
  • MSC (2000): Primary 30F60; Secondary 37F30
  • DOI:
  • MathSciNet review: 2466018