Coarse analyzing metric spaces of non-positive curvature and topological analyzing remainders of its compactifications

这是重要的数学（特别是几何）研究考克斯特群。研究了Coxeter群，得到了非正曲率度量空间和Coxeter群几何作用于其上的双曲空间的边界的拓扑性质。具体地说，我们提供了以下结果：一个必要和充分条件与拓扑分形结构的边界，建设的拓扑泛空间作为边界的Coxeter群，和，推广的分解定理的Coxeter群。此外，我们还研究了与紧化算子的不动点密切相关的映射的染色数，得到了局部有限图上同胚的染色数的一个充要条件.

It is important mathematically (in particular, geometrically) to study Coxeter groups. We investigate Coxeter groups and obtain topological properties for boundaries of metric spaces of non-positive curvature and hyperbolic spaces on whose Coxeter groups are geometrically acted. Specifically, we provide the following results: a necessary and sufficient condition with a topological fractal structure of its boundary, the construction of topological universal spaces as the boundaries of Coxeter groups, and, an extension of the decomposition theorem to the Coxeter group. Moreover, we investigate colorings numbers of maps deeply related to fix points of remainders of compactifications and we obtain a necessary and sufficient condition with colorings numbers of homeomorphisms on locally finite graphs.