Rigidity of group topologies and universal minimal flows (C05)

组拓扑的刚性和通用最小流（C05）

• 批准号: 444035161
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/444035161?language=en
• 关键词: Rigidity; group; topologies; universal; minimal

We will study automatic continuity and universal minimal flows for topological groups acting on geometric objects. First, we focus on rigidity of group topologies, motivated by a question due to Rosendal on the existence of a locally compact infinite group with the automatic continuity property. We want to study this question for Burger–Mozes groups. Furthermore, motivated by a question of Evans–Hubička–Nešetřil, we want to understand when universal minimal flows of kaleidoscopic groups are metrisable. Our methods will involve interactions between group theory, topological dynamics and Ramsey theory.

我们将研究作用于几何对象的拓扑群的自动连续性和泛极小流。首先，我们专注于刚性组拓扑结构，动机的一个问题，由于Rosendal的存在一个局部紧无限群的自动连续性。我们想为Burger-Mozes小组研究这个问题。此外，受Evans-Hubička-Nešetzil问题的启发，我们想了解万花筒群的泛极小流何时是可度量化的。我们的方法将涉及群论，拓扑动力学和拉姆齐理论之间的相互作用。