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Abstract: We study lattices in non-positively curved metric spaces. Borel density isestablished in that setting as well as a form of Mostow rigidity. A converse tothe flat torus theorem is provided. Geometric arithmeticity results areobtained after a detour through superrigidity and arithmeticity of abstractlattices. Residual finiteness of lattices is also studied. Riemannian symmetricspaces are characterised amongst CAT0 spaces admitting lattices in terms ofthe existence of parabolic isometries.



Author: P.-E. Caprace, N. Monod

Source: https://arxiv.org/







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