粗相干的余极限定理及其应用
Colimit theorems for coarse coherence with applications
摘要：
我们建立了度量空间的粗相干性的中心定理-族共极限定理的两个版本。这是一个粗略的几何属性，因此对于具有单词度量的有限生成群来说是明确定义的。众所周知，基本群的粗相干性对于高维流形的分类有重要的意义。族共极限定理是一个持久性定理，它给出了粗凝聚群类的结构。事实上，所有已知的持久性定理都是从族极限定理推导出来的。我们也利用这个定理从这个类中构造新的群。
英文摘要：
We establish two versions of a central theorem, the Family Colimit Theorem, for the coarse coherence property of metric spaces. This is a coarse geometric property and so is well-defined for finitely generated groups with word metrics. It is known that coarse coherence of the fundamental group has important implications for classification of high-dimensional manifolds. The Family Colimit Theorem is one of the permanence theorems that give structure to the class of coarsely coherent groups. In fact, all known permanence theorems follow from the Family Colimit Theorem. We also use this theorem to construct new groups from this class.
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