论文标题
SO_0（1，K+1）和SU（1，K+1）的循环亚组的几何极限
Geometric limits of cyclic subgroups of SO_0(1, k+1) and SU(1, k+1)
论文作者
论文摘要
我们研究等级1组SO_0（1，K+1）和SU（1，K+1）的凸形结合循环亚组的几何极限。我们构建了该基团G的亚组序列的示例，这些序列是通过代数收敛的，其几何极限严格包含代数极限，从而概括了Jorgensen对SO_0的亚组首先描述的示例（1,3）。我们还为SO_0（1，K+1）子组提供了必要的条件，以作为一系列环状亚组的几何极限。然后，我们讨论了此类示例对自由组表示的顺序的概括，以及我们在该环境中的构造的应用。
We study geometric limits of convex-cocompact cyclic subgroups of the rank 1 groups SO_0(1, k+1) and SU(1, k+1). We construct examples of sequences of subgroups of such groups G that converge algebraically and whose geometric limit strictly contains the algebraic limit, thus generalizing the example first described by Jorgensen for subgroups of SO_0(1,3). We also give necessary and sufficient conditions for a subgroup of SO_0(1, k+1) to arise as geometric limit of a sequence of cyclic subgroups. We then discuss generalizations of such examples to sequence of representations of free groups, and applications of our constructions in that setting.
