Finite groups and hyperbolic manifolds

Belolipetsky, M.; Lubotzky, A.

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
• Public URL: https://durham-repository.worktribe.com/output/1593683