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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Automorphisms of the deformation space of a Kleinian group
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by James A. Gentilesco PDF
Trans. Amer. Math. Soc. 248 (1979), 207-220 Request permission

Abstract:

In the following paper, we determine the biholomorphic automorphisms of a cross-product of Teichmüller spaces. This in turn helps us to determine the biholomorphic automorphisms of the deformation space of a Kleinian group using the fact that its holomorphic universal covering space is a cross-product of Teichmüller spaces. Among other interesting results, we show that in general the deformation space is not a homogeneous space.
References
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  • Lipman Bers, Fiber spaces over Teichmüller spaces, Acta Math. 130 (1973), 89–126. MR 430318, DOI 10.1007/BF02392263
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  • Irwin Kra, Deformation spaces, A crash course on Kleinian groups (Lectures at a Special Session, Annual Winter Meeting, Amer. Math. Soc., San Francisco, Calif., 1974) Lecture Notes in Math., Vol. 400, Springer, Berlin, 1974, pp. 48–70. MR 0402122
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  • H. L. Royden, Automorphisms and isometries of Teichmüller space, Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, N.Y., 1969) Ann. of Math. Studies, No. 66, Princeton Univ. Press, Princeton, N.J., 1971, pp. 369–383. MR 0288254
  • H. L. Royden, Remarks on the Kobayashi metric, Several complex variables, II (Proc. Internat. Conf., Univ. Maryland, College Park, Md., 1970) Lecture Notes in Math., Vol. 185, Springer, Berlin, 1971, pp. 125–137. MR 0304694
    • J. A. Gentilesco, Automorphisms of the deformation space of a Kleinian group, Doctoral Dissertation, SUNY, Stony Brook.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 248 (1979), 207-220
  • MSC: Primary 32G15; Secondary 30F40
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0521701-4
  • MathSciNet review: 521701