At infinity of finite-dimensional CAT(0) spaces
Group Theory
2014-05-16 v2 Metric Geometry
Abstract
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.
Cite
@article{arxiv.0810.2895,
title = {At infinity of finite-dimensional CAT(0) spaces},
author = {Pierre-Emmanuel Caprace and Alexander Lytchak},
journal= {arXiv preprint arXiv:0810.2895},
year = {2014}
}
Comments
An erratum filling in a gap in the proof of an application of the main result has been included to the original paper