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

在数学上（特别是几何上）研究考克斯特群是很重要的。研究了Coxeter群，得到了Coxeter群几何作用于非正曲率度量空间和双曲空间边界的拓扑性质。具体地说，我们给出了其边界具有拓扑分形结构的一个充分必要条件，构造了拓扑泛空间作为Coxeter群的边界，并将分解定理推广到Coxeter群。此外，研究了紧化余数不动点深度相关映射的着色数，得到了局部有限图上同胚具有着色数的充分必要条件。

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.