Related papers: Quasiisometric embeddings between right-angled Art…

Let $k$ be a nonarchimedean local field. For any $n\geq 3$, we construct the first examples of robust quasi-isometric embeddings of non-elementary free groups into $\mathsf{GL}_n(k)$ which are not limits of Anosov representations. If…

We propose the systematic study of presentations that can be generalised over a continuous open group monomorphism. Presentations with this property can turn well-known presentations such as those for as orientable surface groups, Artin…

We establish the tracial stability of a certain class of graph products of C*-algebras. This result involves the development of the "pincushion class" of finite graphs. We then apply this result in two ways. The first application yields a…

We define metric bundles/metric graph bundles which provide a purely topological/coarse-geometric generalization of the notion of trees of metric spaces a la Bestvina-Feighn in the special case that the inclusions of the edge spaces into…

Inspired by a recent paper due to Jos\'{e} Luis Garc\'{i}a, we revisit the attempt of Daniel Simson to construct a counterexample to the pure semisimplicity conjecture. Using compactness, we show that the existence of such counterexample…

A finite simple graph \G determines a right-angled Artin group G_\G, with one generator for each vertex v, and with one commutator relation vw=wv for each pair of vertices joined by an edge. The Bestvina-Brady group N_\G is the kernel of…

Motivated by the notion of cusp excursion in geometrically finite hyperbolic manifolds, we define a notion of excursion in any subgroup of a given group, and study its asymptotic distribution for right-angled Artin groups and graph…

We show that the homology of the automorphism group of a right-angled Artin group stabilizes under taking products with any right-angled Artin group.

This paper has three main goals. First, we study fixed subgroups of automorphisms of right-angled Artin and Coxeter groups. If $\varphi$ is an untwisted automorphism of a RAAG, or an arbitrary automorphism of a RACG, we prove that ${\rm…

We prove that the mapping class group of a sphere with five punctures admits uncountably many coarsely equivariant coarse median structures. The same is shown for right-angled Artin groups whose defining graphs are connected, triangle- and…

The present article continues the study of median groups initiated in [6, 9, 10]. Some classes of median groups are introduced and investigated with a stress upon the class of the so called A-groups which contains as remarkable subclasses…

We develop a new criterion to tell if a group $G$ has the maximal gap of $1/2$ in stable commutator length (scl). For amalgamated free products $G = A \star_C B$ we show that every element $g$ in the commutator subgroup of $G$ which does…

Extended admissible groups belong to a particular class of graphs of groups that admit a decomposition generalizing those of non-geometric 3-manifold groups and Croke-Kleiner admissible groups. In this paper, we study several…

For every orientable surface of finite negative Euler characteristic, we find a right-angled Artin group of cohomological dimension two which does not embed into the associated mapping class group. For a right-angled Artin group on a graph…

We provide an extension of the Gromov--Zimmer Embedding Theorem for Cartan geometries of [3] to tractor bundles carrying any invariant connection, including tractor connections and prolongation connections of first BGG operators for…

We characterize twisted right-angled Artin groups whose finitely generated subgroups are also twisted right-angled Artin groups. Additionally, we give a classification of coherence within this class of groups in terms of the defining graph.…

We prove that if a right-angled Artin group $A_\Gamma$ is abstractly commensurable to a group splitting non-trivially as an amalgam or HNN-extension over $\mathbb{Z}^n$, then $A_\Gamma$ must itself split non-trivially over $\mathbb{Z}^k$…

We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let $G$ be a group that is one-ended, hyperbolic relative to…

For all Artin groups, we characterise the girth (i.e. the length of a shortest cycle) of the defining graph algebraically, showing that it is an isomorphism invariant. Using this result, we prove that the Artin groups based on a cycle graph…

The rank of a hierarchically hyperbolic space is the maximal number of unbounded factors in a standard product region. For hierarchically hyperbolic groups, this coincides with the maximal dimension of a quasiflat. Examples for which the…