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Finite groups and hyperbolic manifolds.

Belolipetsky, M. and Lubotzky, A. (2005) 'Finite groups and hyperbolic manifolds.', Inventiones mathematicae., 162 (3). pp. 459-472.


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.

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Record Created:26 Apr 2007
Last Modified:08 Apr 2009 16:30

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