Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 

 

Automorphisms of the deformation space of a Kleinian group


Author: James A. Gentilesco
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] Lipman Bers, Uniformization, moduli, and Kleinian groups, Bull. London Math. Soc. 4 (1972), 257–300. MR 0348097, https://doi.org/10.1112/blms/4.3.257
  • [2] Lipman Bers, Fiber spaces over Teichmüller spaces, Acta. Math. 130 (1973), 89–126. MR 0430318, https://doi.org/10.1007/BF02392263
  • [3] Lipman Bers and Leon Greenberg, Isomorphisms between Teichmüller spaces, 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. 53–79. MR 0289763
  • [4] Clifford J. Earle and Irwin Kra, On isometries between Teichmüller spaces, Duke Math. J. 41 (1974), 583–591. MR 0348098
  • [5] Clifford J. Earle and Irwin Kra, On holomorphic mappings between Teichmüller spaces, Contributions to analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 107–124. MR 0430319
  • [6] 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) Springer, Berlin, 1974, pp. 48–70. Lecture Notes in Math., Vol. 400. MR 0402122
  • [7] Bernard Maskit, Self-maps on Kleinian groups, Amer. J. Math. 93 (1971), 840–856. MR 0291453, https://doi.org/10.2307/2373474
  • [8] 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
  • [9] H. L. Royden, Remarks on the Kobayashi metric, Several complex variables, II (Proc. Internat. Conf., Univ. Maryland, College Park, Md., 1970) Springer, Berlin, 1971, pp. 125–137. Lecture Notes in Math., Vol. 185. MR 0304694
  • [10] J. A. Gentilesco, Automorphisms of the deformation space of a Kleinian group, Doctoral Dissertation, SUNY, Stony Brook.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32G15, 30F40

Retrieve articles in all journals with MSC: 32G15, 30F40


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1979-0521701-4
Keywords: Fuchsian group, Kleinian group, Riemann surface, Teichmüller space, deformation space, modular group, Kobayashi metric, Finsler structure
Article copyright: © Copyright 1979 American Mathematical Society