Deformation of proper actions on reductive homogeneous spaces

作者：Kassel Fanny^*

来源：Mathematische Annalen, 2012, 353(2): 599-632.

DOI：10.1007/s00208-011-0672-1

Let be a real reductive Lie group and a closed reductive subgroup of . We investigate the deformation of compact quotients of /, that is, of quotients of / by discrete groups I%26quot; that are uniform lattices in some closed reductive subgroup of acting properly and cocompactly on /. For of real rank 1, we prove that after a small deformation in , such a group I%26quot; keeps acting properly discontinuously and cocompactly on /. More generally, we prove that the properness of the action of any convex cocompact subgroup of on / is preserved under small deformations, and we extend this result to reductive homogeneous spaces / over any local field. As an application, we obtain compact quotients of SO(2, 2)/U(, 1) by Zariski-dense discrete subgroups of SO(2, 2) acting properly discontinuously.

• 出版日期2012-6