Isometry groups of non-positively curved spaces: Discrete subgroups
We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained after a detour through superrigidity and arithmeticity of abstract lattices. Residual finiteness of lattices is also studied. Riemannian symmetric spaces are characterised amongst CAT(0) spaces admitting lattices in terms of the existence of parabolic isometries.
Keywords: Relatively Hyperbolic Groups ; Semi-Simple Groups ; Irreducible Lattices ; Arithmetic Lattices ; Bounded Cohomology ; Algebraic-Groups ; Amenable Actions ; Hadamard Spaces ; Curvature ; Rigidity
Record created on 2008-10-29, modified on 2016-08-08