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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 |
Description
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.