Topological dynamics of groupoid actions

Pub Date : 2020-11-17 DOI:10.4171/ggd/687
Felipe Flores, M. Măntoiu
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引用次数: 2

Abstract

Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions, but which have to be put in the right setting, there are also new phenomena. Mostly for groupoids whose source map is not open (and there are many), some properties which were equivalent for group actions become distinct in this general framework; we illustrate this with various counterexamples.
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类群作用的拓扑动力学
将拓扑动力学中的一些基本概念和结果推广到拓扑空间中的连续类群作用。我们主要关注递归性质。除了与群体行为的经典案例类似的结果(但必须置于正确的环境中)之外,还有一些新现象。大多数情况下,对于源映射没有打开的groupoid(有很多),一些对群动作等效的属性在这个通用框架中变得不同;我们用各种反例来说明这一点。
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