论文标题
$ \ mathbb {z} $中的第一个具有系数的统一有限同源组，并且在及物案例中其消失的表征
The first uniformly finite homology group with coefficients in $\mathbb{Z}$ and a characterisation of its vanishing in the transitive case
论文作者
论文摘要
我们研究了第一个均匀的Block和Weinberger的有限同源组，以统一有限的图形，并在$ \ Mathbb {Z} $中，系数和$ \ Mathbb {Z} _2 $。当图形是树时，或系数位于$ \ mathbb {z} _2 $中时，将获得该组的表征。在一般情况下，我们描述了三种群体不存在的现象。在横向图的情况下，它们的分离也证明对于不进行逐渐播种也是必要的。
We study the first uniformly finite homology group of Block and Weinberger for uniformly locally finite graphs, with coefficients in $\mathbb{Z}$ and $\mathbb{Z}_2$. When the graph is a tree, or coefficients are in $\mathbb{Z}_2$, a characterisation of the group is obtained. In the general case, we describe three phenomena that entail non-vanishing of the group; their disjunction is shown to also be necessary for non-vanishing in the case of transitive graphs.
