论文标题
类型的半群，比较和几乎有限的群体素
The type semigroup, comparison and almost finiteness for ample groupoids
论文作者
论文摘要
我们证明，当且仅当其类型的半群几乎没有被孔子的情况下，最少的第二个可计数型群体可以进行动力比较。此外，我们调查了几乎有限的群体几乎没有被孔子的半群，在多大程度上，几乎有限的群体素质。最后，我们通过表征粗群的几乎有限性，该桥梁在粗糙的几乎有限的情况下以新型的公制空间不变特性来表征粗糙的类动力学，这可能是在粗几何形状中具有独立的兴趣。结果，我们能够构建几乎没有其他理想特性的几乎有限的主体类型的新示例，例如合理性甚至A-T-t-Menability。这种行为与与小组动作相关的主转换组素的情况形成鲜明对比。
We prove that a minimal second countable ample groupoid has dynamical comparison if and only if its type semigroup is almost unperforated. Moreover, we investigate to what extent a not necessarily minimal almost finite groupoid has an almost unperforated type semigroup. Finally, we build a bridge between coarse geometry and topological dynamics by characterizing almost finiteness of the coarse groupoid in terms of a new coarsely invariant property for metric spaces, which might be of independent interest in coarse geometry. As a consequence, we are able to construct new examples of almost finite principal groupoids lacking other desirable properties, such as amenability or even a-T-menability. This behaviour is in stark contrast to the case of principal transformation groupoids associated to group actions.
