Finite groups and hyperbolic manifolds

Mikhail Belolipetsky*, Alexander Lubotzky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

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.

Original languageEnglish
Pages (from-to)459-472
Number of pages14
JournalInventiones Mathematicae
Volume162
Issue number3
DOIs
StatePublished - Dec 2005

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