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Concept

Groupe libre

Publications associées (15)

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

Approximating nonabelian free groups by groups of homeomorphisms of the real line

Yash Lodha

We show that for a large class C of finitely generated groups of orientation preserving homeomorphisms of the real line, the following holds: Given a group G of rank k in C, there is a sequence of k-markings (G,S-n), n is an element of N whose limit in the ...

2020

Coherent actions by homeomorphisms on the real line or an interval

Yash Lodha

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 PRESS2020

Hyperbolicity as an obstruction to smoothability for one-dimensional actions

Yash Lodha

Ghys and Sergiescu proved in the 1980s that Thompson's group T, and hence F, admits actions by C-infinity diffeomorphisms of the circle. They proved that the standard actions of these groups are topologically conjugate to a group of C-infinity diffeomorphi ...

GEOMETRY & TOPOLOGY PUBLICATIONS2019

Extensive amenability and a Tits alternative for topological full groups

Nóra Gabriella Szoke

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 ...

EPFL2019

The cup product of Brooks quasimorphisms

Nicolas Monod

We prove the vanishing of the cup product of the bounded cohomology classes associated to any two Brooks quasimorphisms on the free group. This is a consequence of the vanishing of the square of a universal class for tree automorphism groups. ...

WALTER DE GRUYTER GMBH2018

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

Nielsen Equivalence In Gupta-Sidki Groups

For a group G generated by k elements, the Nielsen equivalence classes are defined as orbits of the action of AutF(k), the automorphism group of the free group of rank k, on the set of generating k-tuples of G. Let p >= 3 be prime and G(p) the Gupta-Sidki ...

American Mathematical Society (AMS)2017

Fixed 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 ...

2017

Elliptic curves over a finite field and the trace formula

Ian Nicholas Petrow

We prove formulas for power moments for point counts of elliptic curves over a finite field k such that the groups of k-points of the curves contain a chosen subgroup. These formulas express the moments in terms of traces of Hecke operators for certain con ...

Wiley2017

Supramenable groups

Julian Kellerhals

In this thesis we investigate the class of supramenable groups. In the first part we give an overview of some analogous characterizations of amenable and supramenable groups. This is followed by the study of two properties close to supramenability: megamen ...

EPFL2014

Homogeneous number of free generators

We address two questions of Simon Thomas. First, we show that for any n >= 3 one can find a four-generated free subgroup of SLn (Z) which is profinitely dense. More generally, we show that an arithmetic group Gamma that admits the congruence subgroup prope ...

Walter De Gruyter Gmbh2014

On the topological full group of a minimal Cantor Z2-system

Nicolas Monod, Gábor Elek

Grigorchuk and Medynets recently announced that the topological full group of a minimal Cantor Z-action is amenable. They asked whether the statement holds for all minimal Cantor actions of general amenable groups as well. We answer in the negative by prod ...

2013

Stable classical groups and strongly torsion generated groups

Strongly torsion generated groups are those with a single normal generator, of arbitrary finite order. They are useful for realizing sequences of abelian groups as homology groups. Known examples include stable alternating groups and stable groups generate ...

2009

Non-unitarisable representations and random forests

Nicolas Monod

We establish a connection between Dixmier's unitarisability problem and the expected degree of random forests on a group. As a consequence, a residually finite group is non-unitarisable if its first L2-Betti number is non-zero or if it is finitely generate ...

Oxford University Press2009

Publications associées (15)