论文标题
与应用的粗相结合的定理
Colimit theorems for coarse coherence with applications
论文作者
论文摘要
我们为公制空间的粗相连贯性质建立了两个中央定理的族定理定理。这是一个粗糙的几何特性，因此对于具有单词指标的有限生成的组定义了。众所周知，基本组的粗糙连贯性对高维流形的分类具有重要意义。家族定理是赋予粗糙群体类别结构的永久定理之一。实际上，所有已知的永久定理都来自家庭定理。我们还使用此定理来构建该课程的新组。
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.
