Rank-one isometries of proper CAT(0)-spaces

Abstract

Let G be a non-elementary group of isometries of a proper CAT(0)-space with limit set L. We survey properties of the action of G on L under the assumption that G contains a rank-one element. Among others, we show that there is a dense orbit for the action of G on the complement of the diagonal in LxL and that pairs of fixed points of rank-one elements are dense in the complement of the diagonal of LxL.

Several corrections; to appear in Contemp. Math

References in corpus (4)

• Isometry groups of non-positively curved spaces: structure theory
• Rank one isometries of buildings and quasi-morphisms of Kac-Moody groups
• Isometry groups of proper CAT(0)-spaces
• Some properties of non-positively curved lattices

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• On equivariant homeomorphisms of boundaries of CAT(0) groups
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• Existence and non-existence of bounded packing in CAT(0) spaces and Gromov hyperbolic spaces