On Splitting Theorems for Cat(0) Spaces and Compact Geodesic Spaces of Non-positive Curvature
نویسنده
چکیده
In this paper, we prove some splitting theorems for CAT(0) spaces on which some product group acts geometrically and show a splitting theorem for compact geodesic spaces of nonpositive curvature. A CAT(0) group Γ is said to be rigid, if Γ determines the boundary up to homeomorphism of a CAT(0) space on which Γ acts geometrically. Croke and Kleiner have constructed a non-rigid CAT(0) group. As an application of the splitting theorems for CAT(0) spaces, we obtain that if Γ1 and Γ2 are rigid CAT(0) groups then so is Γ1 ×Γ2, and the boundary ∂(Γ1 ×Γ2) is homeomorphic to the join ∂Γ1 ∗ ∂Γ2 of the boundaries of Γ1 and Γ2.
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