Mathematics – Group Theory
Scientific paper
2009-11-22
Mathematics
Group Theory
25 pages
Scientific paper
Let G be a real reductive Lie group and H a closed reductive subgroup of G. We investigate the deformation of "standard" compact quotients of G/H, i.e., of quotients of G/H by discrete subgroups Gamma of G that are uniform lattices in a closed reductive subgroup L of G acting properly and cocompactly on G/H. For L of real rank 1, we prove that after a small deformation in G, such a group Gamma remains discrete in G and its action on G/H remains properly discontinuous and cocompact. More generally, we prove that the properness of the action of any convex cocompact subgroup of L on G/H is preserved under small deformations, and we extend this result to reductive homogeneous spaces G/H over any local field. As an application, we obtain compact quotients of SO(2n,2)/U(n,1) by Zariski-dense discrete subgroups of SO(2n,2) acting properly discontinuously.
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