At infinity of finite-dimensional CAT(0) spaces

Details At infinity of finite-dimensional CAT(0) spaces At infinity of finite-dimensional CAT(0) spaces

2008-10-16

arxiv.org/abs/0810.2895v1

Math. Ann. 346 Nr. 1 (2010), pp. 1-21.

Mathematics

Group Theory

19 pages

Scientific paper

10.1007/s00208-009-0381-1

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 $ \bar{X} = X \cup \bd 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.

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