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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
Posted:
May 5, 2006
MathSciNet review:
2231632
Full-text PDF Free Access
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Abstract: For any countable group  whatsoever, there is a complete hyperbolic surface whose isometry group is  .
References
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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
Email:
allcock@math.utexas.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08460-7
PII:
S 0002-9939(06)08460-7
Received by editor(s):
May 4, 2005
Posted:
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 after
28 years from publication.
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