论文标题
Matui的AH猜想用于图形素
Matui's AH conjecture for Graph Groupoids
论文作者
论文摘要
我们证明，Matui的AH猜想适用于无限图的图形类型。这是一个猜想，将植物类固醇的拓扑完整组与群体的同源性联系在一起。我们的主要结果补充了Matui在有限案例中的结果，这使得AH猜想是对所述猜想假设所涵盖的所有图形组的构想。此外，我们观察到，对于任意图，图组的同源性与其groupoid $ c^*$ - 代数的$ k $理论相吻合。
We prove that Matui's AH conjecture holds for graph groupoids of infinite graphs. This is a conjecture which relates the topological full group of an ample groupoid with the homology of the groupoid. Our main result complements Matui's result in the finite case, which makes the AH conjecture true for all graph groupoids covered by the assumptions of said conjecture. Furthermore, we observe that for arbitrary graphs, the homology of a graph groupoid coincides with the $K$-theory of its groupoid $C^*$-algebra.
