Related papers: A generalization of the Davis-Moussong complex for…

In his work on the Novikov conjecture, Yu introduced Property $A$ as a readily verified criterion implying coarse embeddability. Studied subsequently as a property in its own right, Property $A$ for a discrete group is known to be…

We develop an analogy between right-angled Artin groups and mapping class groups through the geometry of their actions on the extension graph and the curve graph respectively. The central result in this paper is the fact that each…

This paper is a short survey on four basic questions on Artin-Tits groups: the torsion, the center, the word problem, and the cohomology ($K(\pi,1)$ problem). It is also an opportunity to prove three new results concerning these questions:…

We develop a battery of tools for studying quasi-isometric rigidity and classification problems for splittings of groups. The techniques work best for finite graphs of groups where all edge and vertex groups are coarse PD groups. For…

We define the braid groups of a two-dimensional orbifold and introduce conventions for drawing braid pictures. We use these to realize the Artin groups associated to the spherical Coxeter diagrams A_n, B_n=C_n and D_n and the affine…

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…

This work explores the topological properties of virtual Artin groups, a recent extension of the ``virtual" concept - initially developed for braids - to all Artin groups, as introduced by Bellingeri, Paris, and Thiel. For any given Coxeter…

We introduce a novel algebraic structure called di-skew brace by which we show that generalized digroups systematically yield bijective, non-degenerate solutions to the set-theoretic Yang-Baxter equation. We study the structural properties…

We prove that finite index subgroups of right angled Artin groups are conjugacy separable. We then apply this result to establish various properties of other classes of groups. In particular, we show that any word hyperbolic Coxeter group…

We give an explicit construction of a maximal torsion-free finite-index subgroup of a certain type of Coxeter group. The subgroup is constructed as the fundamental group of a finite and non-positively curved polygonal complex. First we…

A Coxeter system is an ordered pair (W,S) where S is the generating set in a particular type of presentation for the Coxeter group W. A subgroup of W is called special if it is generated by a subset of S. Amalgamated product decompositions…

We introduce shortcut graphs and groups. Shortcut graphs are graphs in which cycles cannot embed without metric distortion. Shortcut groups are groups which act properly and cocompactly on shortcut graphs. These notions unify a surprisingly…

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…

We introduce a method for analyzing the convex hull of a set in non-positively curved piecewise Euclidean polygonal complexes and we apply this method to prove that, with the usual action of Fm x Zn on the metric product of the Cayley graph…

For group actions on hyperbolic CAT(0) square complexes, we show that the acylindricity of the action is equivalent to a weaker form of acylindricity phrased purely in terms of stabilisers of points, which has the advantage of being much…

We develop the theory of Poisson and Dirac manifolds of compact types, a broad generalization in Poisson and Dirac geometry of compact Lie algebras and Lie groups. We establish key structural results, including local normal forms, canonical…

We investigate a novel diagrammatic approach to examining strict actions of a Coxeter group or a braid group on a category. This diagrammatic language, which was developed in a series of papers by Elias, Khovanov and Williamson, provides…

In this article we study combinatorial non-positive curvature aspects of various simplicial complexes with natural $\widetilde A_n$ shaped simplicies, including Euclidean buildings of type $\widetilde A_n$ and Cayley graphs of Garside…

Let $\Gamma$ be a simplicial, finite, connected graph such that $\Gamma$ does not decompose as a nontrivial join. We prove that two notions of strong quasiconvexity and stability are equivalent in the right-angled Artin group $A_\Gamma$…

We define an operation on finite graphs, called co-contraction. By showing that co-contraction of a graph induces an injective map between right-angled Artin groups, we exhibit a family of graphs, without any induced cycle of length at…