Related papers: A classification of right-angled Coxeter groups wi…

We provide conditions on the defining graph of a right-angled Coxeter group presentation that guarantees the boundary of any CAT(0) space on which the group acts geometrically will be locally connected. This is a revised version of a…

This paper introduces a new class of right-angled Coxeter groups with totally disconnected Morse boundaries. We construct this class recursively by examining how the Morse boundary of a right-angled Coxeter group changes if we glue a graph…

In this paper we study CAT(0) groups and their splittings as graphs of groups. For one-ended CAT(0) groups with isolated flats we prove a theorem characterizing exactly when the visual boundary is locally connected. This characterization…

We investigate the planarity of the boundaries of right-angled Coxeter groups. We show that non-planarity of the defining graph does not necessarily imply non-planarity of every boundary of the associated right-angled Coxeter group,…

We compute Aut(W) for any even Coxeter group whose Coxeter diagram is connected, contains no edges labeled 2, and cannot be separated into more than 2 connected components by removing a single vertex. The description is given explicitly in…

We show that any split extension of a right-angled Coxeter group $W_{\Gamma}$ by a generating automorphism of finite order acts faithfully and geometrically on a $\mathrm{CAT}(0)$ metric space.

We provide geometric conditions on a pair of hyperplanes of a CAT(0) cube complex that imply divergence bounds for the cube complex. As an application, we classify all right-angled Coxeter groups with quadratic divergence and show…

In this paper, we study CAT(0) groups and Coxeter groups whose boundaries are scrambled sets. Suppose that a group $G$ acts geometrically (i.e. properly and cocompactly by isometries) on a CAT(0) space $X$. (Such group $G$ is called a {\it…

It is an open question whether right-angled Coxeter groups have unique group-equivariant visual boundaries. Croke and Kleiner present a right-angled Artin group with more than one visual boundary. In this paper we present a right-angled…

In this paper, we show that the boundary $\partial\Sigma(W,S)$ of a right-angled Coxeter system $(W,S)$ is minimal if and only if $W_{\tilde{S}}$ is irreducible, where $W_{\tilde{S}}$ is the minimum parabolic subgroup of finite index in…

We investigate the combinatorial and geometric properties of automorphism groups of universal right-angled Coxeter groups, which are the automorphism groups of free products of copies of Z_2. It is currently an open question as to whether…

We study the algebraic rank of various classes of $\mathrm{CAT}(0)$ groups. They include right-angled Coxeter groups, right-angled Artin groups, relatively hyperbolic groups and groups acting geometrically on $\mathrm{CAT}(0)$ spaces with…

We place conditions on the presentation graph of a right-angled Artin group that guarantee the standard CAT(0) cube complex on which the group acts geometrically has non-path-connected boundary.

We study fixed point properties of the automorphism group of the universal Coxeter group Aut$(W_n)$. In particular, we prove that whenever Aut$(W_n)$ acts by isometries on complete $d$-dimensional CAT$(0)$ space with…

An odd Coxeter group $W$ is one which admits a Coxeter system $(W,S)$ for which all the exponents $m_{ij}$ are either odd or infinity. The paper investigates the family of odd Coxeter groups whose associated labeled graphs…

We consider the question of determining whether a given group (especially one generated by involutions) is a right-angled Coxeter group. We describe a group invariant, the involution graph, and we characterize the involution graphs of…

Let $C(L)$ be the right-angled Coxeter group defined by an abstract triangulation $L$ of $\mathbb{S}^2$. We show that $C(L)$ is isomorphic to a hyperbolic right-angled reflection group if and only if $L$ can be realized as an acute…

We study the automorphisms of graph products of cyclic groups, a class of groups that includes all right-angled Coxeter and right-angled Artin groups. We show that the group of automorphism generated by partial conjugations is itself a…

We show that every graph product of finitely generated abelian groups acts properly and cocompactly on a CAT(0) cubical complex. The complex generalizes (up to subdivision) the Salvetti complex of a right-angled Artin group and the Coxeter…

Shephard groups are common generalizations of Coxeter groups, Artin groups, and graph products of cyclic groups. Their definition is similar to that of a Coxeter group, but generators may have arbitrary order rather than strictly order 2.…