Finite groups and hyperbolic manifolds

• 成果类型: Article
• 署名作者: Belolipetsky, M; Lubotzky, A
• 署名单位: Hebrew University of Jerusalem; Russian Academy of Sciences
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-005-0446-z
• 发表日期: 2005
• 页码: 459-472
• 关键词: normal automorphisms

摘要

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.