不可分解连续统Higson冠
Indecomposable continua as Higson coronae
摘要：
本文考虑了Higson冕是不可分解连续统的空间。证明了对于一个非紧的真度量空间$X$，它是粗测地的，具有粗有界几何，$X$的Higson冠是不可分解连续统当且仅当$X$粗等价于自然数空间.然后，利用Higson冠的分量的可分解性和不可分解性，给出了具有单端和双端的有限生成群的特征.我们把它刻画成一个群，它的Higson冠是两个不可分解连续统的拓扑和。
英文摘要：
In this paper, we consider spaces whose Higson coronae are indecomposable continua. We show that for a non-compact proper metric space $X$ which is coarsely geodesic and has coarse bounded geometry, the Higson corona of $X$ is an indecomposable continuum if and only if $X$ is coarsely equivalent to the space of natural numbers. Then we give characterizations of finitely generated groups that have one or two ends by decomposability/indecomposability of the components of their Higson coronae. we characterize it as a group whose Higson corona is a topological sum of two indecomposable continua.
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