Skew-amenability of topological groups

  • Kate Juschenko

    University of Texas at Austin, USA
  • Friedrich Martin Schneider

    TU Bergakademie Freiberg, Germany
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Abstract

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 and Monod’s group of piecewise projective homeomorphisms of the real line.

Cite this article

Kate Juschenko, Friedrich Martin Schneider, Skew-amenability of topological groups. Comment. Math. Helv. 96 (2021), no. 4, pp. 805–851

DOI 10.4171/CMH/525