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AN OBSTRUCTION TO l(p)-DIMENSION

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Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Masato Mimura

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 ...

2019

An upper bound for the Tarski numbers of nonamenable groups of piecewise projective homeomorphisms

Yash Lodha

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 Ltd2017

Representing groups against all odds

Maxime Gheysens

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 ...

EPFL2017

Variations on a theme by Higman

Nicolas Monod

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. ...

Elsevier2017

An indiscrete Bieberbach theorem: from amenable CAT$(0)$ groups to Tits buildings

Nicolas Monod

Non-positively curved spaces admitting a cocompact isometric action of an amenable group are investigated. A classification is established under the assumption that there is no global fixed point at infinity under the full isometry group. The visual bounda ...

2015

Amenable hyperbolic groups

Nicolas Monod

We give a complete characterization of the locally compact groups that are nonelementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover gi ...

European Mathematical Soc2015

Actions of amenable equivalence relations on CAT(0) fields

Martin Anderegg, Philippe Paul Antoine Henry

We present the general notion of Borel fields of metric spaces and show some properties of such fields. Then we make the study specific to the Borel fields of proper CAT(0) spaces and we show that the standard tools we need behave in a Borel way. We also i ...

Cambridge University Press2014

Cantor systems, piecewise translations and simple amenable groups

Nicolas Monod

We provide the first examples of finitely generated simple groups that are amenable (and infinite). This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by constructing a suita ...

Annal Mathematics2013

Fixed points and amenability in non-positive curvature

Nicolas Monod

Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the torsion-free case. We est ...

Springer2013

Non-Supramenable Groups Acting On Locally Compact Spaces

Nicolas Monod, Julian Kellerhals

Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UC ...

Univ Bielefeld2013