Related papers: Every Coxeter group acts amenably on a compact spa…

Let $G$ be a group that admits a cocompact classifying space for proper actions $X$. We derive a formula for the Bredon cohomological dimension for proper actions of $G$ in terms of the relative cohomology with compact support of certain…

Let $X$ be a non-degenerate connected compact metric space. If $X$ admits a distal minimal action by a finitely generated amenable group, then the first \vCech cohomology group $ {\check H}^1(X)$ with integer coefficients is nontrivial. In…

We provide involutory symmetric generating sets of finitely generated Coxeter groups, fulfilling a suitable finiteness condition, which in particular is fulfilled in the finite, affine and compact hyperbolic cases.

In this note, we show that if $G$ is an amenable group acting on a dendrite $X$, then the restriction of $G$ to any minimal set $K$ is equicontinuous, and $K$ is either finite or homeomorphic to the Cantor set.

Let $K$ be a locally compact field of characteristic 0. Let $G$ be a linear algebraic group defined over $K$, acting algebraically on an algebraic variety $V$. We prove that the action of $G(K)$ (the group of $K$-rational points of $G$) on…

We prove that for any coarse spaces $X_1,\dots,X_n$ of asymptotic dimension $\ge 1$, the product $X=X_1\times\dots\times X_n$ has asymptotic dimension $\ge n$. Another result states that a finitary coare space $Z$ has $\mathrm{asdim}(Z)\ge…

In this paper we study the right-angled Coxeter groups that acts geometrically on the Salvetti complex of a certain right-angled Artin group, which we refer to as Croke-Kleiner spaces. We prove that any right-angled Coxeter group that acts…

We prove that finitely generated amenable groups acting on CAT(0) spaces satisfy the following alternative: either every action on a geodesically complete CAT(0) space with bounded geometry (or finite dimension) has a global fixed point, or…

Let (G,S) be a Coxeter group. We construct a continuation, to the open unit disc, of the unitary representations associated to the positive definite functions g -> r^l(g). (Here 0<r<1, and l denotes the length function with respect to the…

We prove that every acylindrically hyperbolic group admits a minimal and extremely proximal action on a compact metrizable space. If there are no nontrivial finite normal subgroups, then the action is topologically free. This answers…

We prove that every topological action of a countable group on a metrizable space can be realized as a bi-Lipschitz action with respect to some compatible metric. This extends a result due to U. Hamenst\"{a}dt regarding finitely generated…

We introduce the notion of Zimmer amenability for actions of discrete quantum groups on von Neumann algebras. We prove generalizations of several fundamental results of the theory in the noncommutative case. In particular, we give a…

We show that if G is an infinitely generated locally (polycyclic-by-finite) group with cohomology almost everywhere finitary, then every finite subgroup of G acts freely and orthogonally on some sphere.

Inspired by a classical theorem of topological dimension theory, we prove that every geodesic metric space of asymptotic dimension $n$ containing a bi-infinite geodesic can be coarsely separated by a subset $S$ of asymptotic dimension equal…

In this paper we introduce the galaxy of Coxeter groups -- an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between Coxeter systems. In doing so, we would like to suggest a new framework to…

We show that for a countable discrete group which is locally of finite asymptotic dimension, the generic continuous action on Cantor space has hyperfinite orbit equivalence relation. In particular, this holds for free groups, answering a…

We introduce a notion of entropy for automorphisms of discrete groups which admit amenable actions on a compact space. This entropy is dual to classical topological entropy in the sense that if G is discrete and abelian then our notion of…

We show that the dynamic asymptotic dimension of a minimal free action of an infinite virtually cyclic group on a compact Hausdorff space is always one. This extends a well-known result of Guentner, Willett, and Yu for minimal free actions…

We prove that any countable non-amenable group G admits a free minimal amenable purely infinite action on the non-compact Cantor set. This answers a question of Kellerhals, Monod and R{\o}rdam.

A right-angled Coxeter group is a group with a given set of generators of order two, subject only to the relations that certain pairs of the generators commute. Various papers have shown how homological properties of the Coxeter group are…