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Nicolas Monod

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Publications associées (46)

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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

AN OBSTRUCTION TO l(p)-DIMENSION

Nicolas Monod, Henrik Densing Petersen

Let G be any group containing an infinite elementary amenable subgroup and let 2 < p < infinity. We construct an exhaustion of l(p) G by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obst ...

Annales Inst Fourier2014

A note on topological amenability

Nicolas Monod

A simple characterisation of topological amenability in terms of bounded cohomology is proved, following Johnson's formulation of amenability. The connection to injective Banach modules is established. ...

Oxford University Press2010

The norm of the Euler class

Nicolas Monod

We prove that the norm of the Euler class

\mathcal{E}

for flat vector bundles is

2^{-n}

(in even dimension

n

, since it vanishes in odd dimension). This shows that the Sullivan-Smillie bound considered by Gromov and Ivanov-Turaev is sharp. We construc ...

Springer Verlag2012

Lie groups in the symmetric group: Reducing Ulam's problem to the simple case

Nicolas Monod

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 ...

Academic Press Inc Elsevier Science2023

Product groups acting on manifolds

Nicolas Monod

We analyse volume-preserving actions of product groups on Riemannian manifolds. Under a natural spectral irreducibility assumption, we prove the following dichotomy: Either the action is measurably isometric, in which case there are at most two factors; or ...

2009

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

A fixed point theorem for L1 spaces

Nicolas Monod

We prove a fixed point theorem for a family of Banach spaces, notably for L^1. Applications include the optimal answer to the "derivation problem" for group algebras which originated in the 1960s. ...

Springer-Verlag2012

A family of exotic group C*-algebras

Nicolas Monod

We show that a large family of groups without non-abelian free subgroups satisfy the following strengthening of nonamenability: they each have a rich supply of irreducible representations defining exotic C* -algebras. The construction is explicit. (c) 2024 ...

Academic Press Inc Elsevier Science2024

Groups of piecewise projective homeomorphisms

Nicolas Monod

The group of piecewise projective homeomorphisms of the line provides straightforward torsion-free counterexamples to the so-called von Neumann conjecture. The examples are so simple that many additional properties can be established. ...

National Academy of Sciences2013

Decomposing locally compact groups into simple pieces

Nicolas Monod

We present a contribution to the structure theory of locally compact groups. The emphasis is put on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic cocompact sub ...

Cambridge University Press2011

Equivariant measurable liftings

Nicolas Monod

We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Mobius group of the projective line. Since the general proof is very simple but not explicit, we also provi ...

Polish Acad Sciences Inst Mathematics-Impan2015

An Exotic Deformation of the Hyperbolic Space

Nicolas Monod

Let Isom(H^n) be the group of isometries of the n-dimensional real hyperbolic space. We first classify all continuous non-elementary actions of on the infinite-dimensional real hyperbolic space. We then prove the existence of a continuous family of non-iso ...

Johns Hopkins Univ Press2014

Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms

Nicolas Monod

Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite permutation group ...

POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN2019

Some comments on piecewise-projective groups of the line

Nicolas Monod

We consider groups of piecewise-projective homeomorphisms of the line which are known to be non-amenable using notably the Carrière–Ghys theorem on ergodic equivalence relations. Replacing that theorem by an explicit fixed-point argument, we can strengthen ...

2025

Gelfand pairs admit an Iwasawa decomposition

Nicolas Monod

Every Gelfand pair (G, K) admits a decomposition G = K P, where P < G is an amenable subgroup. In particular, the Furstenberg boundary of G is homogeneous. Applications include the complete classification of non-positively curved Gelfand pairs, relying on ...

SPRINGER HEIDELBERG2020

Lamplighters and the bounded cohomology of Thompson's group

Nicolas Monod

We prove the vanishing of the bounded cohomology of lamplighter groups for a wide range of coefficients. This implies the same vanishing for a number of groups with self-similarity properties, such as Thompson's group F. In particular, these groups are bou ...

SPRINGER BASEL AG2022

Asymptotics of Cheeger constants and unitarisability of groups

Nicolas Monod

Given a group Gamma, we establish a connection between the unitarisability of its uniformly bounded representations and the asymptotic behaviour of the isoperimetric constants of Cayley graphs of Gamma for increasingly large generating sets. The connection ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Extreme points in non-positive curvature

Nicolas Monod

A natural analogue of the Krein-Milman theorem is shown to fail for CAT(0) spaces. ...

Polish Acad Sciences Inst Mathematics-Impan2016

Relative amenability

Nicolas Monod

We introduce a relative fixed point property for subgroups of a locally compact group, which we call relative amenability. It is a priori weaker than amenability. We establish equivalent conditions, related among others to a problem studied by Reiter in 19 ...

European Mathematical Soc2014