On equivariant homeomorphisms of boundaries of CAT(0) groups

2010/04/25 by Tetsuya Hosaka, Hosaka, Tetsuya · 1 citation
Mathematics · #20F65 #57M07 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:20F65 #msc:57M07

paper · pdf · doi:10.48550/arxiv.1004.4376

15 pages

openalex publication_date 2010/04/25 · arxiv created 2010/11/28 · arxiv updated 2010/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate an equivariant homeomorphism of the boundaries ∂ X and ∂ Y of two proper CAT(0) spaces X and Y on which a CAT(0) group G acts geometrically. We provide a sufficient condition to obtain a G-equivariant homeomorphism of the two boundaries ∂ X and ∂ Y as a continuous extension of the quasi-isometry ϕ:Gx₀→ Gy₀ defined by ϕ(gx₀)=gy₀, where x₀∈ X and y₀∈ Y.

Citations

• Parabolic subgroups of Coxeter groups acting by reflections on CAT(0) spaces

Cited by

• On equivariant homeomorphisms of boundaries of CAT(0) groups and Coxeter groups

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