The Michigan Mathematical Journal

The action of geometric automorphisms of asymptotic Teichmüller spaces

Ege Fujikawa

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Michigan Math. J. Volume 54, Issue 2 (2006), 269-282.

First available: 23 August 2006

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Zentralblatt MATH identifier

Primary: 30F60: Teichmüller theory [See also 32G15]
Secondary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx] 37F30: Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems


Fujikawa, Ege. The action of geometric automorphisms of asymptotic Teichmüller spaces. The Michigan Mathematical Journal 54 (2006), no. 2, 269--282. doi:10.1307/mmj/1156345593.

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  • L. Ahlfors, Conformal invariants, McGraw-Hill, New York, 1973.
  • C. J. Bishop, Quasiconformal mapping of Y-pieces, Rev. Mat. Iberoamericana 18 (2002), 627--652.
  • C. J. Earle, F. P. Gardiner, and N. Lakic, Teichmüller spaces with asymptotic conformal equivalence, preprint, Inst. Hautes Études Sci., 1995.
  • ------, Asymptotic Teichmüller space, Part I: The complex structure, Contemp. Math., 256, pp. 17--38, Amer. Math. Sci., Providence, RI, 2000.
  • ------, Asymptotic Teichmüller space, Part II: The metric structure, Contemp. Math., 355, pp. 187--219, Amer. Math. Soc., Providence, RI, 2004.
  • C. J. Earle, V. Markovic, and D. Saric, Barycentric extension and the Bers embedding for asymptotic Teichmüller space, Contemp. Math., 311, pp. 87--105, Amer. Math. Soc., Providence, RI, 2002.
  • A. Epstein, Effectiveness of Teichmüller modular groups, Contemp. Math., 256, pp. 69--74, Amer. Math. Soc., Providence, RI, 2000.
  • E. Fujikawa, Limit sets and regions of discontinuity of Teichmüller modular groups, Proc. Amer. Math. Soc. 132 (2004), 117--126.
  • ------, Modular groups acting on infinite dimensional Teichmüller spaces, Contemp. Math., 355, pp. 239--253, Amer. Math. Soc., Providence, RI, 2004.
  • E. Fujikawa and K. Matsuzaki, Recurrent and periodic points for isometries of $L^\infty$ spaces, Indiana Univ. Math. J. 55 (2006).
  • E. Fujikawa, H. Shiga, and M. Taniguchi, On the action of the mapping class group for Riemann surfaces of infinite type, J. Math. Soc. Japan 56 (2004), 1069--1086.
  • F. P. Gardiner, Teichmüller theory and quadratic differentials, Wiley, New York, 1987.
  • F. P. Gardiner and N. Lakic, Quasiconformal Teichmüller theory, Math. Surveys Monogr., 76, Amer. Math. Soc., Providence, RI, 2000.
  • F. P. Gardiner and D. P. Sullivan, Symmetric structure on a closed curve, Amer. J. Math. 114 (1992), 683--736.
  • K. Matsuzaki, The infinite direct product of Dehn twists acting on infinite dimensional Teichmüller spaces, Kodai Math. J. 26 (2003), 279--287.
  • ------, A countable Teichmüller modular group, Trans. Amer. Math. Soc. 357 (2005), 3119--3131.
  • ------, A quasiconformal mapping class group acting trivially on the asymptotic Teichmüller space, Proc. Amer. Math. Soc. (to appear).
  • ------, Dynamics of Teichmüller modular groups and general topology of moduli spaces, preprint.
  • S. Nag, The complex analytic theory of Teichmüller spaces, Wiley, New York, 1988.
  • A. Vasil'ev, Moduli of families of curves for conformal and quasiconformal mappings, Lecture Notes in Math., 1788, Springer-Verlag, Berlin, 2002.
  • S. A. Wolpert, The length spectra as moduli for compact Riemann surfaces, Ann. of Math. (2) 109 (1979), 323--351.