Amenable actions preserving a locally finite metric - Archive ouverte HAL Access content directly
Journal Articles Expositiones Math. Year : 2018

Amenable actions preserving a locally finite metric


The class A of countable groups that admit a faithful, transitive, amenable – in the sense that there is an invariant mean – action on a set has been widely investigated in the past. In this paper, we no longer require the action to be transitive, but we ask for it to preserve a locally finite metric (and still to be faithful and amenable). The groups having such actions are those that embed into a totally disconnected amenable locally compact group. Then we focus on the subclass A 1 of groups for which the actions are moreover transitive. This class is strictly contained into A and includes non-amenable groups. An important particular case of actions preserving a locally finite metric is given by actions by automorphisms of locally finite connected graphs. We take this opportunity, in our partly expository paper, to review some nice results about amenable actions in this setting.
Fichier principal
Vignette du fichier
Ananth-Memorial-Issue.v2.pdf (215.1 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01767131 , version 1 (15-04-2018)



Claire Anantharaman-Delaroche. Amenable actions preserving a locally finite metric. Expositiones Math., 2018, ⟨10.1016/j.exmath.2018.06.002⟩. ⟨hal-01767131⟩
59 View
160 Download



Gmail Facebook X LinkedIn More