Skew-amenability of topological groups
COMMENTARII MATHEMATICI HELVETICI(2021)
摘要
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 isometrics and automorphisms, clarify the connection with extensive amenability of group actions, establish a Folner-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.
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关键词
Topological group, group action, amenability, extensive amenability, isometry group
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