Uniform research of topological Kleinian groups by using geometric limits

本研究的目的是证明一些基本定理来统一解释拓扑Kleinian群论的主要结果。特别地，我们对Kleinian群的几何极限的拓扑和几何分类感兴趣。在我们的研究之前，这种分类只对承认代数极限的特殊Kleinian群（如拟fuchsian群）的序列进行。通过这个项目，我们成功地分类了具有相同拓扑类型且不一定在代数上收敛的几何有限Kleinian群序列的拓扑极限和几何极限。此外，作为一个应用，我们证明了几何极限的结束层合定理。

The aim of this research is to prove fundamental theorems to explain uniformly main results on topological Kleinian group theory. In particular, we are interested in the topological and geometrical classifications of geometric limits of Kleinian groups. Before our research, this classification was done only for sequences of special Kleinian groups (e.g. quasi-Fuchsian groups) which admit algebraic limits. Though this project, we have succeeded in classifying topologically and geometrically geometric limits of an sequences of geometrically finite Kleinian groups which have the same topological type which do not necessarily converge algebraically. Moreover, as an application, we have proved that the Ending Lamination Theorem for geometric limits.