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

2008/10/21 by Ursula Hamenstaedt, Hamenstaedt, Ursula · 3 citations
Mathematics · #20F67 #53C20 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.0810.3794

openalex publication_date 2008/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Rank one isometries of buildings and quasi-morphisms of Kac-Moody groups

Cited by

• An extreme boundary of acylindrically hyperbolic groups
• Boundary actions of CAT(0) spaces: topological freeness and applications to C^*-algebras
• Isometry groups of proper CAT(0)-spaces

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