Dynamics of the Action of a CAT(0) Group on the Boundary
Dynamics of the Action of a CAT(0) Group on the Boundary
复制标题
CAT(0) 群体在边界上的行动动态
DOI：
10.1023/a:1010301824765
复制
发表时间：
2001
影响因子：
0.5
通讯作者：
K. Ruane
中科院分区：
文献类型：
--
作者：
K. Ruane
本文的主要定理给出了CAT(0)群的两个双曲等距不动点集的一个几何条件，保证由两个元素生成的子群包含一个自由子群。第3节中的结果表明，当且仅当元素在CAT(0)群中几乎处于中心位置时，元素扩展到边界上的恒等。最后，本文最后一节讨论了二维情况，并证明了两个双曲等距的幂当且仅当不动点集上的一个几何条件满足时可交换。
The main theorem here gives a geometric condition on the fixed point sets of two hyperbolic isometries of a CAT(0) group which guarantees that the subgroup generated by the two elements contains a free subgroup. A result in section 3 shows that an element extends to the identity on the boundary if and only if the element is virtually central in the CAT(0) group. Finally, the two dimensional case is considered in the last section of the paper and there it is shown that powers of two hyperbolic isometries commute if and only if a geometric condition on the fixed point sets is satisfied.