Croke-Kleiner容许群：性质（QT）和拟凸性
Croke-Kleiner admissible groups: Property (QT) and quasiconvexity
摘要：
Croke-Kleiner容许群是由Croke-Kleiner首先引入的一类特殊的群的图，它推广了$3$ -维图流形的基本群.本文证明了：如果$G$是Croke-Kleiner容许群，几何地作用在CAT（0）空间$X$上，则$G$的一个生成子群具有有限高当且仅当它是强拟凸的.我们还表明，如果$G \curvearrowright X$是一个翻转CKA行动，那么$G$是拟等距嵌入到一个有限的产品的准树。通过对翻转CKA作用$G \curvearrowright X$顶点群的进一步假设，证明了$G$满足Bestvina-Bromberg-Fujiwara引入的性质（QT）.
英文摘要：
Croke-Kleiner admissible groups firstly introduced by Croke-Kleiner belong to a particular class of graph of groups which generalize fundamental groups of $3$--dimensional graph manifolds. In this paper, we show that if $G$ is a Croke-Kleiner admissible group, acting geometrically on a CAT(0) space $X$, then a finitely generated subgroup of $G$ has finite height if and only if it is strongly quasi-convex. We also show that if $G \curvearrowright X$ is a flip CKA action then $G$ is quasi-isometric embedded into a finite product of quasi-trees. With further assumption on the vertex groups of the flip CKA action $G \curvearrowright X$, we show that $G$ satisfies property (QT) that is introduced by Bestvina-Bromberg-Fujiwara.
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