On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature

Tetsuya Hosaka

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arXiv · math/0405551

On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature

Tetsuya Hosaka

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Abstract

In this paper, we show some splitting theorems for CAT(0) spaces on which a product group acts geometrically and we obtain a splitting theorem for compact geodesic spaces of non-positive curvature. A CAT(0) group $Γ$ is said to be {\it rigid}, if $Γ$ determines the boundary up to homeomorphisms of a CAT(0) space on which $Γ$ acts geometrically. C.Croke and B.Kleiner have constructed a non-rigid CAT(0) group. As an application of the splitting theorems for CAT(0) spaces, we obtain that if $Γ_1$ and $Γ_2$ are rigid CAT(0) groups then so is $Γ_1\times Γ_2$.

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BibTeX RIS

Tetsuya Hosaka. 2010-05-23. On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature. https://arxiv.org/abs/math/0405551

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