Cat(0) Groups and Coxeter Groups Whose Boundaries Are Scrambled Sets
نویسنده
چکیده
In this paper, we study CAT(0) groups and Coxeter groups whose boundaries are scrambled sets. Suppose that a group G acts geometrically (i.e. properly and cocompactly by isometries) on a CAT(0) space X. (Such group G is called a CAT(0) group.) Then the group G acts by homeomorphisms on the boundary ∂X of X and we can define a metric d∂X on the boundary ∂X. The boundary ∂X is called a scrambled set if for any α, β ∈ ∂X with α 6= β, (1) lim sup{d∂X(gα, gβ) | g ∈ G} > 0 and (2) lim inf{d∂X(gα, gβ) | g ∈ G} = 0. We investigate when are boundaries of CAT(0) groups (and Coxeter groups) scrambled sets.
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