# Mathematics Colloquia and Seminars

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### Finite groups and hyperbolic manifolds

**Geometry/Topology**

Speaker: | Misha Belolipetsky, Hebrew University |

Location: | 693 Kerr |

Start time: | Wed, Mar 9 2005, 4:10PM |

The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show that for every n > 1, 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 and Kojima, respectively. Our proof is non-constructive: it uses counting results from subgroup growth theory and the strong approximation theorem to show that such manifolds exist. This is a joint work A. Lubotzky.