论文标题
无限图的纯映射类组的粗略几何形状
Coarse Geometry of Pure Mapping Class Groups of Infinite Graphs
论文作者
论文摘要
我们讨论了由algom-kfir-bestvina的最新作品以及Mann-Rafi在映射Infinite型表面的大型几何形状上的大规模几何形状的纯粹的局部有限图，无限图的纯制图类别的大规模几何形状。使用玫瑰多框架进行非局部紧凑组的粗几何形状，我们将何时在局部有限的无限图的纯映射类组中进行分类（紧凑的类似物），并且何时是局部粗糙的界限（局部紧凑的类似物）。我们的技术为某些图提供了纯映射类组的第一个积分共同体，并允许我们计算所有本地界限的无限等级图的所有本地界限纯映射类组的渐近维度。该维度总是零或无限。
We discuss the large-scale geometry of pure mapping class groups of locally finite, infinite graphs, motivated by recent work of Algom-Kfir--Bestvina and the work of Mann--Rafi on the large-scale geometry of mapping class groups of infinite-type surfaces. Using the framework of Rosendal for coarse geometry of non-locally compact groups, we classify when the pure mapping class group of a locally finite, infinite graph is globally coarsely bounded (an analog of compact) and when it is locally coarsely bounded (an analog of locally compact). Our techniques give lower bounds on the first integral cohomology of the pure mapping class group for some graphs and allow us to compute the asymptotic dimension of all locally coarsely bounded pure mapping class groups of infinite rank graphs. This dimension is always either zero or infinite.
