n splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature
n splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature
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CAT(0) 空间和非正曲率紧测地空间的 n 分裂定理
DOI：
10.1007/s00209-011-0972-x
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发表时间：
2012
影响因子：
0.8
通讯作者：
Tetsuya Hosaka
中科院分区：
文献类型：
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作者：
Atsushi Ishii;Yeonhee Jang;Kanako Oshiro;Atsushi Ishii;Atsushi Ishii;Atsushi Ishii;Atsushi Ishii;石井敦;Keiichi Sakai;Keiichi Sakai;山口祥司;山口祥司;境圭一;境圭一;境圭一;境圭一;境圭一;境圭一;Tetsuya Hosaka;Tetsuya Hosaka;Naotsugu Chinen and Tetsuya Hosaka;Tetsuya Hosaka
本文给出了乘积群几何作用于其上的CAT（0）空间的几个分裂定理，并得到了非正曲率紧致测地空间的一个分裂定理。一个CAT（0）群Γ称为Berigid，如果Γ确定了它的边界直到一个CAT（0）空间的同胚，而Γ在该空间上作几何作用。C.克罗克和B。Kleiner构造了一个非刚性CAT（0）群。作为CAT（0）空间的分裂定理的应用，我们得到了：如果Γ 1和Γ 2是刚性CAT（0）群，那么Γ1× Γ2也是刚性CAT（0）群.
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 berigid, if Γ determines its 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 Γ1and Γ2are rigid CAT(0) groups then so is Γ1× Γ2.