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Finite groups and hyperbolic manifolds

Belolipetsky, M.; Lubotzky, A.

Authors

M. Belolipetsky

A. Lubotzky



Abstract

The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show that for every n≥2, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n=2 and n=3 have been proven by Greenberg (1974) and Kojima (1988), respectively. Our proof is non constructive: it uses counting results from subgroup growth theory to show that such manifolds exist.

Citation

Belolipetsky, M., & Lubotzky, A. (2005). Finite groups and hyperbolic manifolds. Inventiones Mathematicae, 162(3), 459-472. https://doi.org/10.1007/s00222-005-0446-z

Journal Article Type Article
Publication Date 2005-12
Deposit Date Apr 26, 2007
Journal Inventiones Mathematicae
Print ISSN 0020-9910
Electronic ISSN 1432-1297
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 162
Issue 3
Pages 459-472
DOI https://doi.org/10.1007/s00222-005-0446-z