At infinity of finite-dimensional CAT(0) spaces

By P. Caprace, A. Lytchak. 2008

59 citations recorded by the source corpus.

We show that any filtering family of closed convex subsets of a finite-dimensional CAT(0) space X has a non-empty intersection in the visual bordification $${ \overline{X} = X \cup \partial X}$$ . Using this fact, several results known for proper CAT(0) spaces may be extended to finite-dimensional spaces, including the existence of canonical fixed points at infinity for parabolic isometries, algebraic and geometric restrictions on amenable group actions, and geometric superrigidity for non-elementary actions of irreducible uniform lattices in products of locally compact groups.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/174ac16fe4786ac063599b511d9e3224152e99a8

How researchers see this paper

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In Geometry and Topology

1. Michah Sageev
2. P. Caprace
3. Denis V. Osin
4. Anthony Genevois
5. Mark F. Hagen
6. Alessandro Sisto
7. Daan Krammer
8. Ruth Charney

In Mathematical Physics

1. Michah Sageev
2. P. Caprace
3. Denis V. Osin
4. Anthony Genevois
5. Mark F. Hagen
6. Alessandro Sisto
7. Ruth Charney
8. Harold Sultan

Citations in the corpus

• Rank Rigidity for Cat(0) Cube Complexes (2010, methodology): “Proof of Corollary G. It follows from [ CLy , Th. 1.7] that Γ is amenable if and only if it is {locally finite}-by-{virtually Abelian}.”