Isometry groups of non‐positively curved spaces: discrete subgroups
By P. Caprace, Nicolas Monod. 2009
81 citations recorded by the source corpus.
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 super‐rigidity and arithmeticity of abstract lattices. Residual finiteness of lattices is also studied. Riemannian symmetric spaces are characterized amongst CAT(0) spaces admitting lattices in terms of the existence of parabolic isometries.
Subfields: Civil and Structural Engineering, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/96a900e698b5aec16df0005e9679e8e4b3bc65df
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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Civil and Structural Engineering
In Geometry and Topology
- Michah Sageev
- A. Nevo
- Koichi Nagano
- Tobias Hartnick
- A. Lytchak
- Mark F. Hagen
- Denis V. Osin
- Alessandro Sisto
In Mathematical Physics
- Michah Sageev
- Koichi Nagano
- M. Bjorklund
- A. Nevo
- Tobias Hartnick
- A. Lytchak
- Denis V. Osin
- Mark F. Hagen
Citations in the corpus
- Approximate lattices (2016, background): “Nevo for pointing out the references [15] and [17] respectively.”
- The Poisson boundary of CAT(0) cube complex groups (2011, background): “ X P X E. We wish to obtain a corresponding splitting of G; that is, we aim to show that uniform lattices in Aut(X) are reducible. Such a result is true in a much more general setting, due to work of [CM]. In our setting, the matter is simplied by the following fact. Lemma 2.7. Let Xbe a Euclidean c”
- Geodesically complete spaces with an upper curvature bound (2018, background): “Finally, geodesic completeness plays an important role in geometric group theory, see, for instance, [CM09], [GS17].”