论文标题
离散的本地有限的完整组canter设置同态同态
Discrete locally finite full groups of Cantor set homeomorphisms
论文作者
论文摘要
这项工作是出于为分段完整组找到本地紧凑的群体拓扑的问题（又称拓扑完整组）。我们确定在我们在此处介绍的确切意义上，在cantor集的一组自动塑性群体上紧凑型拓扑中局部紧凑的任何分段完整组都必须均匀离散。 Cantor集的自我塑性统一的群体在紧凑型拓扑中尤其是可计数的，局部有限的，残留有限的和离散的。由此产生的分段完整组构成了克里格（Krieger）引入的丰富小组的子类。我们通过它们的曲折图和相关的维度范围（$ k_0 $ $组）来确定这些组的结构。我们通过一个示例表明，并非所有均匀离散的分段完整组都是``显而易见''的子组的子组，即分段完整的有限组。
This work is motivated by the problem of finding locally compact group topologies for piecewise full groups (a.k.a.~ topological full groups). We determine that any piecewise full group that is locally compact in the compact-open topology on the group of self-homeomorphisms of the Cantor set must be uniformly discrete, in a precise sense that we introduce here. Uniformly discrete groups of self-homeomorphisms of the Cantor set are in particular countable, locally finite, residually finite and discrete in the compact-open topology. The resulting piecewise full groups form a subclass of the ample groups introduced by Krieger. We determine the structure of these groups by means of their Bratteli diagrams and associated dimension ranges ($K_0$ groups). We show through an example that not all uniformly discrete piecewise full groups are subgroups of the ``obvious'' ones, namely, piecewise full groups of finite groups.
