3 research outputs found
At infinity of finite-dimensional CAT(0) spaces
We show that any filtering family of closed convex subsets of a
finite-dimensional CAT(0) space has a non-empty intersection in the visual
bordification . 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.Comment: An erratum filling in a gap in the proof of an application of the
main result has been included to the original pape