Corpus ID: 231934019

Wreath products of groups acting with bounded orbits

  title={Wreath products of groups acting with bounded orbits},
  author={P. Leemann and G. Schneeberger},
If S is a structure over (a concrete category over) metric spaces, we say that a group G has property BS if any action on a S-space has bounded orbits. Examples of such structures include metric spaces, Hilbert spaces, CAT(0) cube complexes, connected median graphs, trees or ultra-metric spaces. The corresponding properties BS are respectively Bergman’s property, property FH (which, for countable groups, is equivalent to the celebrated Kazhdan’s property (T)), property FW (both for CAT(0) cube… Expand


On Property (FA) for wreath products
Abstract We characterize permutational wreath products with Property (FA). For instance, we show that the standard wreath product A ≀ B of two non-trivial countable groups A and B has Property (FA)Expand
Spaces with measured walls, the Haagerup property and property (T)
We introduce the notion of a space with measured walls, generalizing the concept of a space with walls due to Haglund and Paulin (Simplicité de groupes d'automorphismes d'espaces à courbure négative.Expand
Property FW and wreath products of groups: a simple approach using Schreier graphs
The group property FW stands in-between the celebrated Kazdhan’s property (T) and Serre’s property FA. Among many characterizations, it might be defined, for finitely generated groups, as having allExpand
Relative property (T) and related properties of wreath products
Let H and Γ be two discrete groups and X be a set on which Γ acts. We investigate when the wreath product H≀XΓ has relative property (T) and give a complete characterization of property (T) for suchExpand
Strongly Bounded Groups and Infinite Powers of Finite Groups
We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recentlyExpand
Metric graph theory and geometry: a survey
The article surveys structural characterizations of several graph classes defined by distance properties, which have in part a general algebraic flavor and can be interpreted as subdirectExpand
New examples of groups acting on real trees
We construct the first example of a finitely generated group which has Serre's property (FA) (i.e., whenever it acts on a simplicial tree it fixes a vertex), but admits a fixed point-free action onExpand
Kazhdan and Haagerup properties from the median viewpoint
Abstract We prove the existence of a close connection between spaces with measured walls and median metric spaces. We then relate properties (T) and Haagerup (a-T-menability) to actions on medianExpand
Lamplighter groups, median spaces, and a-T-menability
This paper is dedicated to the proof of the following statement: the wreath product of two groups acting metrically properly on median spaces acts metrically properly on some median space we callExpand
Kazhdan’s Property (T)
Let G be a locally compact (second countable) group and π:G → U(ℋ) a unitary representation of G on the (separable) Hilbert space ℋ.Of course,ℋ may or may not contain non-trivial vectors invariantExpand