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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Pure mapping class group acting on Teichmüller space
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by Ege Fujikawa PDF
Conform. Geom. Dyn. 12 (2008), 227-239 Request permission

Abstract:

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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Additional Information
  • Ege Fujikawa
  • Affiliation: Department of Mathematics, Chiba University, 1-33 Yayoi-cho, Inage, Chiba, 263-8522, Japan
  • MR Author ID: 706593
  • Email: fujikawa@math.s.chiba-u.ac.jp
  • 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: https://doi.org/10.1090/S1088-4173-08-00188-4
  • MathSciNet review: 2466018