Related papers: On the virtually-cyclic dimension of surface braid…

We study the algebraic structure of the automorphism group of a general right-angled Artin group. We show that this group is virtually torsion-free and has finite virtual cohomological dimension. This generalizes results proved by the…

We prove that an Artin group splits over infinite cyclic subgroups if and only if its defining graph has a separating vertex, and explicitly construct a JSJ decomposition over infinite cyclic subgroups for all Artin groups. We then use…

There exist right angled Artin groups $A$ such that the isomorphism problem for finitely presented subgroups of $A$ is unsolvable, and for certain finitely presented subgroups the conjugacy and membership problems are unsolvable. It follows…

In this paper, we sharpen a theorem of Artin to show that for a finite group, the dimension of the subspace of class functions spanned by the rational valued characters equals the number of conjugacy classes of cyclic subgroups.

We prove that an arbitrary right-angled Artin group $G$ admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree. Consequently, $G$ admits quasi-isometric group embeddings into a pure…

We study product set growth in groups with acylindrical actions on quasi-trees and, more generally, hyperbolic spaces. As a consequence, we show that for every surface $S$ of finite type, there exist $\alpha,\beta>0$ such that for any…

A result of Allock [1](arXiv:math/9907194) states that certain orbifold braid groups contain Artin groups of type $D_n$, $\tilde{B}_n$ and $\tilde{D}_n$ as finite index subgroups. The underlying orbifolds have at most two cone points of…

We study a quotient of the group algebra of the braid group in which the Artin generators satisfy a cubic relation. This quotient is maximal among the ones satisfying such a cubic relation. It is finite-dimensional for at least n at most 5…

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…

We give a complete characterisation of when the right-angled Artin group on one cycle graph can be quasiisometrically embedded in the right-angled Artin group on another cycle graph. In particular, we find infinitely many instances of…

We define and study extensions of Artin's representation and braid monodromy representation to the case of topological and algebraical generalisations of braid groups. In particular we provide faithful representations of braid groups of…

Given a group G, we consider its classifying space for the family of virtually cyclic subgroups. We show for many groups, including for example, one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and CAT(0) cube groups,…

We consider the group of unrestricted virtual braids, describe its structure and explore its relations with fused links. Also, we define the groups of flat virtual braids and virtual Gauss braids and study some of their properties, in…

Let $n\geq 3$. In this paper we deal with the conjugacy problem in the Artin braid group quotient $B_n/[P_n,P_n]$. To solve it we use systems of equations over the integers arising from the action of $B_n/[P_n,P_n]$ over the abelianization…

We derive a lower bound on the size of finite non-cyclic quotients of the braid group that is superexponential in the number of strands. We also derive a similar lower bound for nontrivial finite quotients of the commutator subgroup of the…

Twin groups and virtual twin groups are planar analogues of braid groups and virtual braid groups, respectively. These groups play the role of braid groups in the Alexander-Markov correspondence for the theory of stable isotopy classes of…

We construct an embedding of any right-angled Artin group $G(\Delta)$ defined by a graph $\Delta$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $\Delta$. This construction…

We study the outer automorphism group of a right-angled Artin group A_G in the case where the defining graph G is connected and triangle-free. We give an algebraic description of Out(A_G) in terms of maximal join subgraphs in G and prove…

We define the intersection complex for the universal cover of a compact weakly special square complex and show that it is a quasi-isometry invariant. By using this quasi-isometry invariant, we study the quasi-isometric classification of…

Consider a one-ended word-hyperbolic group. If it is the fundamental group of a graph of free groups with cyclic edge groups then either it is the fundamental group of a surface or it contains a finitely generated one-ended subgroup of…