Concept
Amenable group
Related publications (31)
Lie groups in the symmetric group: Reducing Ulam's problem to the simple case
Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...
San Diego2023Coherent actions by homeomorphisms on the real line or an interval
We study actions of groups by orientation preserving homeomorphisms on R (or an interval) that are minimal, have solvable germs at +/-infinity and contain a pair of elements of a certain dynamical type. We call such actions coherent. We establish that such ...
HEBREW UNIV MAGNES PRESS2020Extensive amenability and a Tits alternative for topological full groups
This dissertation investigates the amenability of topological full groups using a property of group actions called extensive amenability. Extensive amenability is a core concept of several amenability results for groups of dynamical origin. We study its pr ...
EPFL2019Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings
The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups. In this Part II, we prove that a disjoint union ...
2019Extensive amenability and an application to interval exchanges
Nicolas Monod, Nicolas Matte Bon
Extensive amenability is a property of group actions which has recently been used as a tool to prove amenability of groups. We study this property and prove that it is preserved under a very general construction of semidirect products. As an application, w ...
2018Representing groups against all odds
We investigate how probability tools can be useful to study representations of non-amenable groups. A suitable notion of "probabilistic subgroup" is proposed for locally compact groups, and is valuable to induction of representations. Nonamenable groups ad ...
EPFL2017An upper bound for the Tarski numbers of nonamenable groups of piecewise projective homeomorphisms
The Tarski number of a nonamenable group is the smallest number of pieces needed for a paradoxical decomposition of the group. Nonamenable groups of piecewise projective homeomorphisms were introduced in [N. Monod, Groups of piecewise projective homeomorph ...
World Scientific Publ Co Pte Ltd2017Variations on a theme by Higman
We propose elementary and explicit presentations of groups that have no amenable quotients and yet are SQ-universal. Examples include groups with a finite K (pi,1), no Kazhdan subgroups and no Haagerup quotients. ...
Elsevier2017Fixed Points For Bounded Orbits In Hilbert Spaces
Nicolas Monod, Maxime Gheysens
Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact a-compact groups (e.g., countabl ...
Elsevier2017Traces on reduced group C-*-algebras
In this short note we prove that the reduced group C-*-algebra of a locally compact group admits a non-zero trace if and only if the amenable radical of the group is open. This completely answers a question raised by Forrest, Spronk and Wiersma. ...
Wiley2017