Mostow-Margulis rigidity with locally compact targets

Abstract

Let $ \Gamma $ be a lattice in a simple higher rank Lie group G. We describe all locally compact (not necessarily Lie) groups H in which $ \Gamma $ (with the only exception of non-uniform lattices in $ G \simeq {\rm SL_2}({\Bbb R}) $ , which are virtually free groups) we give a similar description of all possible locally compact groups H, in which $ \Gamma $ can be embedded as a uniform lattice.