Related papers: The Tits alternative for CAT(0) cubical complexes

We exhibit 3-generator Artin groups which have finite 2-dimensional Eilenberg-Mac Lane spaces, but which do not act properly discontinuously by semi-simple isometries on a 2-dimensional CAT(0) complex. We prove that infinitely many of these…

Quasi-free actions of finite groups on Cuntz algebras $\mathcal O_n$ for $n\geq 2$ are classified up to conjugacy by data in the representation ring. Partial results are obtained for quasi-free actions by compact groups.

Let $G$ be a finite group and $\alpha(G)=\frac{|C(G)|}{|G|}$\,, where $C(G)$ denotes the set of cyclic subgroups of $G$. In this short note, we prove that $\alpha(G)\leq\alpha(Z(G))$ and we describe the groups $G$ for which the equality…

We bound the size of $d$-dimensional cubulations of finitely presented groups. We apply this bound to obtain acylindrical accessibility for actions on CAT(0) cube complexes and bounds on curves on surfaces.

We study discrete groups from the view point of a dimension gap in connection to CAT(0) geometry. Developing studies by Brady-Crisp and Bridson, we show that there exist finitely presented groups of geometric dimension 2 which do not act…

We study certain actions of finitely generated abelian groups on higher dimensional noncommutative tori. Given a dimension $d$ and a finitely generated abelian group $G$, we apply a certain function to detect whether there is a simple…

It is known that a finite group G can only act freely on affine n-space if K has positive characteristic p and G is a p-group. In that case the group action is "non-linear" and the ring of regular functions must be a trace-surjective…

In this paper, we study isometric actions on finite-dimensional CAT(0) spaces for the Higman-Thompson groups $T_n$, which are generalizations of Thompson's group $T$. It is known that every semi-simple action of $T$ on a complete CAT(0)…

We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors and associated subdirect products.…

Following Isaacs (see [Isa08, p. 94]), we call a normal subgroup N of a finite group G large, if $C_G(N) \leq N$, so that N has bounded index in G. Our principal aim here is to establish some general results for systematically producing…

We consider diagram groups as defined by V. Guba and M. Sapir. A diagram group G acts on the associated cube complex K by isometries. It is known that if a cube complex L is of a finite dimension then every isometry g of L is semi-simple,…

We specify exactly which groups can act geometrically on CAT(0) spaces whose visual boundary is homeomorphic to either a circle or a suspension of a Cantor set.

We establish obstructions for groups to act by homeomorphisms on dendrites. For instance, lattices in higher rank simple Lie groups will always fix a point or a pair. The same holds for irreducible lattices in products of connected groups.…

We study free and compact group actions on unital C*-algebras. In particular, we provide a complete classification theory of these actions for compact Abelian groups and explain its relation to the classical classification theory of…

Whenever the mapping class group of a closed orientable surface of genus g acts by semisimple isometries on a complete CAT(0) space of dimension less than g it fixes a point.

In 1960 Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases. In this paper we address…

We construct finitely generated torsion-free solvable groups $G$ that have infinite rank, but such that all finitely generated torsion-free metabelian subquotients of $G$ are virtually abelian. In particular all finitely generated…

We study the acylindrical hyperbolicity of groups acting by isometries on CAT(0) cube complexes, and obtain simple criteria formulated in terms of stabilisers for the action. Namely, we show that a group acting essentially and…

We investigate the cocompact action of Higman's group on a CAT(0) square complex associated to its standard presentation. We show that this action is in a sense intrinsic, which allows for the use of geometric techniques to study the…

We show that if a group $G$ acting faithfully on a rooted tree $T$ has a free subgroup, then either there exists a point $w$ of the boundary $\partial T$ and a free subgroup of $G$ with trivial stabilizer of $w$, or there exists…