标题： 可见空间的蒂茨选择性 显示英文标题

标题： The Tits alternative for visibility spaces

摘要： 设$\Gamma$是一个在满足有界包装性质的可见 CAT(0) 空间$X$上以适当不连续的方式通过等距作用的有限生成群。我们证明$\Gamma$满足蒂茨替代性：它或者是几乎幂零的，或者包含一个秩为$2$的非交换自由子群。在前一种情况下，它等价于$\Gamma$在$X$的几何边界中的极限集的基数不超过$2$。作为蒂茨替代性的应用，我们证明任何在这样的空间上以适当不连续的方式通过等距作用的有限生成扭群必须是一个有限群，并且有一个全局固定点。 显示英文摘要

摘要： Let $\Gamma$ be a finitely generated group acting properly discontinuously by isometries on a visibility CAT(0) space $X$ that satisfies the bounded packing property. We prove that $\Gamma$ satisfies the Tits alternative: it is either almost nilpotent or contains a free nonabelian subgroup of rank $2$. In the former case, it is equivalent to that the cardinality of the limit set of $\Gamma$ in the geometric boundary of $X$ is no greater than $2$. As an application of the Tits alternative, we show that any finitely generated torsion group acting properly discontinuously by isometries on such a space must be a finite group and have a global fixed point.