论文标题
拓扑组的偏斜性
Skew-amenability of topological groups
论文作者
论文摘要
我们研究了偏斜的拓扑组，即那些在伯巴基（Bourbaki）意义上左均匀连续的左右函数空间上承认左右平均值的拓扑组。我们证明了异态和自动形态拓扑组的偏斜性表征，阐明了与集体作用的广泛舒适性，建立Følner-type表征的联系，并讨论偏斜偏度拓扑组的封闭特性。此外，我们隔离了偏斜性的动力充足条件，并在转换组的背景下提供了该标准的几种具体变化。然后，这些结果用于决定偏向于汤普森的$ f $或MONOD的一组真实行的塑料同构的拓扑组的许多示例。
We study skew-amenable topological groups, i.e., those admitting a left-invariant mean on the space of bounded real-valued functions left-uniformly continuous in the sense of Bourbaki. We prove characterizations of skew-amenability for topological groups of isometries and automorphisms, clarify the connection with extensive amenability of group actions, establish a Følner-type characterization, and discuss closure properties of the class of skew-amenable topological groups. Moreover, we isolate a dynamical sufficient condition for skew-amenability and provide several concrete variations of this criterion in the context of transformation groups. These results are then used to decide skew-amenability for a number of examples of topological groups built from or related to Thompson's group $F$ and Monod's group of piecewise projective homeomorphisms of the real line.
