Isometry groups of non-positively curved spaces: discrete subgroups

Details Isometry groups of non-positively curved spaces: discrete subgroups Isometry groups of non-positively curved spaces: discrete subgroups

2009-01-08

arxiv.org/abs/0901.1022v1

See final version in: Journal of Topology 2 No. 4 (2009) 701--746

Mathematics

Group Theory

This is the second of a pair of two articles, originally posted on September 2, 2008 as arXiv:0809.0457v1 For the first part,

Scientific paper

10.1112/jtopol/jtp027

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.

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