TY - JOUR
T1 - Finite groups and hyperbolic manifolds
AU - Belolipetsky, Mikhail
AU - Lubotzky, Alexander
PY - 2005/12
Y1 - 2005/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=27744453883&partnerID=8YFLogxK
U2 - 10.1007/s00222-005-0446-z
DO - 10.1007/s00222-005-0446-z
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AN - SCOPUS:27744453883
SN - 0020-9910
VL - 162
SP - 459
EP - 472
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 3
ER -