相关论文: Proper actions of lamplighter groups associated wi…

From any two median spaces $X,Y$, we construct a new median space $X \circledast Y$, referred to as the diadem product of $X$ and $Y$, and we show that this construction is compatible with wreath products in the following sense: given two…

This article is dedicated to the asymptotic geometry of wreath products $F\wr H := \left( \bigoplus_H F \right) \rtimes H$ where $F$ is a finite group and $H$ a one-ended finitely presented group. Our main result is a complete…

Let $\Lambda$ be an ordered abelian group, $\mathrm{Aut}^+(\Lambda)$ the group of order-preserving automorphisms of $\Lambda$, $G$ a group and $\alpha:G\to\mathrm{Aut}^+(\Lambda)$ a homomorphism. An $\alpha$-affine action of $G$ on a…

We calculate the exact values of the F{\o}lner function $\mathrm{F{\o}l}$ of the lamplighter group $\mathbb{Z}\wr\mathbb{Z}/2\mathbb{Z}$ for the standard generating set. More generally, for any finite group $D$ and $n\geq|D|$, we obtain the…

We study the properly discontinuous and isometric actions on the unit sphere of infinite dimensional Hilbert spaces and we get some new examples of Hilbert manifold with costant positive sectional curvature. We prove some necessary…

We show that a wreath product of two finitely generated abelian groups is LERF. Consequently the free metabelian groups are LERF.

We prove that the properties of acting metrically properly on some space with walls or some CAT(0) cube complex are closed by taking the wreath product with \Z. We also give a lower bound for the (equivariant) Hilbert space compression of…

We show that any free product of two countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite…

In this paper, we show that hyperbolic groups admit proper affine isometric actions on $l^p$-spaces.

We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of…

We prove that if a finite group $G$ has a representation with fixity $f$, then it acts freely and homologically trivially on a finite CW-complex homotopy equivalent to a product of $f+1$ spheres. This shows, in particular, that every finite…

We prove that if a subgroup $H$ of the automorphism group $\mathrm{Aut}(\Sigma^{\mathbb{Z}})$ of a non-trivial full shift acts on points of finite support with a free orbit, then for every finitely-generated abelian group $A$, the abstract…

In this paper, we show that if a group acts isometrically on a good hyperbolic space of finite volume entropy through a non-elementary action, then it admits an affine action on some $L^p$ -space with an unbounded orbit for sufficiently…

A group is called $\Lambda$-free if it has a free Lyndon length function in an ordered abelian group $\Lambda$, which is equivalent to having a free isometric action on a $\Lambda$-tree. A group has a regular free length function in…

In the 1980's K.S. Brown proved that the Houghton group $H_n$ is of type $\operatorname{F}_{n-1}$ but not $\operatorname{FP}_n$. We show that, provided $n\ge3$, the same conclusion holds for all subgroups $G$ of $H_n$ that are 'large' in…

Let $(M,\omega)$ be a connected symplectic manifold on which a connected Lie group $G$ acts properly and in a Hamiltonian fashion with moment map $\mu:M \lra \mf g^*$. Our purpose is investigate multiplicity-free actions, giving criteria to…

In this article, we introduce halo products as a natural generalisation of wreath products. They also encompass lampshuffler groups $\mathrm{FSym}(H) \rtimes H$ and lampcloner groups $\mathrm{FGL}(H) \rtimes H$, as well as many possible…

Let $G$ and $H$ be two groups acting on path connected topological spaces $X$ and $Y$ respectively. Assume that $H$ is finite of order $m$ and the quotient maps $p:X\to X/G$ and $q:Y\to Y/H$ are regular coverings. Then it is well-known that…

We show that for any group $G$ that is hyperbolic relative to subgroups that admit a proper affine isometric action on a uniformly convex Banach space, then $G$ acts properly on a uniformly convex Banach space as well.

We prove that the topological full group $[[X]]$ of a two-sided full shift $X = \Sigma^{\mathbb{Z}}$ contains every right-angled Artin group (also called a graph group). More generally, we show that the family of subgroups with "linear…