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Hyperbolic surfaces with prescribed infinite symmetry groups

Author: Daniel Allcock
Journal: Proc. Amer. Math. Soc. 134 (2006), 3057-3059
MSC (2000): Primary 51M09; Secondary 20F99
Published electronically: May 5, 2006
MathSciNet review: 2231632
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Abstract | References | Similar Articles | Additional Information

Abstract: For any countable group $ G$ whatsoever, there is a complete hyperbolic surface whose isometry group is $ G$.

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

  • 1. M. Belolipetsky and A. Lubotzky, Finite Groups and Hyperbolic Manifolds, Invent. Math. 162 (2005) 459-472. MR 2198218
  • 2. L. Greenberg, Maximal groups and signatures, Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973), Ann. of Math. Studies, No. 79, Princeton University Press, 1974, pp. 207-226. MR 0379835 (52:740)
  • 3. S. Kojima, Isometry transformations of hyperbolic 3-manifolds, Topology and its Applications 29 (1988) 297-307. MR 0953960 (90c:57033)
  • 4. D. D. Long and A. W. Reid, On asymmetric hyperbolic manifolds, Math. Proc. Camb. Phil. Soc. 138:2 (2005) 301-306. MR 2132171
  • 5. W. Thurston, Three-dimensional geometry and topology, ed. Silvio Levy, Princeton Mathematical Series, 35, Princeton University Press, 1997. MR 1435975 (97m:57016)

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Additional Information

Daniel Allcock
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712

Received by editor(s): May 4, 2005
Published electronically: May 5, 2006
Additional Notes: This work was partially supported by NSF grant DMS-024512.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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