Uniform research of topological Kleinian groups by using geometric limits

本研究的目的是证明基本定理，以统一解释拓扑Kleinian群论的主要结果。特别是，我们感兴趣的拓扑和几何分类的几何极限的克莱因集团。在我们的研究之前，这种分类只适用于允许代数极限的特殊Kleinian群（例如拟Fuchsian群）的序列。通过这个项目，我们成功地分类拓扑和几何几何极限的序列几何有限Kleinian群具有相同的拓扑类型，不一定代数收敛。作为应用，我们还证明了几何极限的终结层定理。

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.