arXiv research

Study minimal volume entropy for free-by-cyclic groups and 2D right-angled Artin groups.

Uniqueness of quasi-roots explored in right-angled Artin groups.

This paper characterizes a specific type of twisted Artin groups embedded in knot groups.

New right-angled Artin subgroups found in Artin groups.

Surveying connections between graph combinatorics and algebraic right-angled Artin groups.

We survey the role of right-angled Artin groups in the theory of diffeomorphism groups of low dimensional manifolds. We first describe some of the subgroup structure of right-angled Artin groups. We then discuss the interplay between algebraic structure, compactness, and regularity for group actions on one--dimensional…

Right-angled Artin groups are classified based on measure equivalence.

Proves Gromov's conjecture for a specific type of groups.

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 right-angled Artin group acts acylindrically on its extension graph. From this result we …

Explicitly generates right-angled Artin subgroups from mapping classes.

Study on finiteness property of right-angled Artin groups actions on extension graphs.

We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.

Embedding right-angled Artin groups in mapping class groups of nonorientable surfaces.

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 $\gam$ to embed into the mapping class group of a surface $S$, we show that the …

We give a necessary and sufficient condition for a graph to have a right-angled Artin group as its braid group for braid index $\ge 5$. In order to have the necessity part, graphs are organized into small classes so that one of homological or cohomological characteristics of right-angled Artin groups can be applied. Fi…

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.

We introduce the class of perturbed right-angled Artin groups. These are constructed by gluing Bieri double groups into standard right-angled Artin groups. As a first application of this construction we obtain families of CAT(0) groups containing finitely presented subgroups which are not of type $\mathrm{FP}_3$, and h…

New graph Hamiltonicity via cohomology of Artin groups.

The study examines subgroups of RACGs and RAAGs, focusing on their RAAG properties.

We give an explicit formula for the cohomology of a right angled Artin group with group ring coefficients in terms of the cohomology of its defining flag complex.

Right-angled Artin groups have unique quasi-isometry classes when measure equivalent.

In this note we give the quasi-isometry classification for a class of right angled Artin groups. In particular, we obtain the first such classification for a class of Artin groups with dimension larger than 2; our families exist in every dimension.

Improved bounds on acylindricity for right-angled Artin groups.

Study shows RAAG automorphisms and outer automorphisms are not relatively hyperbolic.

Suppose that $(W,S)$ is a Coxeter system with associated Artin group $A$ and with a simplicial complex $L$ as its nerve. We define the notion of a "standard abelian subgroup" in $A$. The poset of such subgroups in $A$ is parameterized by the poset of simplices in a certain subdivision $L_\oslash$ of $L$. This complex o…

We determine the factorial growth rate of the number of finite index subgroups of right-angled Artin groups as a function of the index. This turns out to depend solely on the independence number of the defining graph. We also make a conjecture for right-angled Coxeter groups and prove that it holds in a limited setting…

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 geometrically on the Croke-Kleiner spaces acts with $π/2$ angles between reflect…

In all known examples of a CAT(0) group acting on CAT(0) spaces with non-homeomorphic CAT(0) visual boundaries, the boundaries are each not path connected. In this paper, we show this does not have to be the case by providing examples of right-angled Artin groups which exhibit non-unique CAT(0) boundaries where all of …

Consider the mapping class group $\Mod_{g,p}$ of a surface $Σ_{g,p}$ of genus $g$ with $p$ punctures, and a finite collection $\{f_1,...,f_k\}$ of mapping classes, each of which is either a Dehn twist about a simple closed curve or a pseudo-Anosov homeomorphism supported on a connected subsurface. In this paper we prov…

We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group $A(K)$ has such a subgroup if its defining graph $K$ contains an $n$-hole (i.e. an induced cycle of length $n$) with $n\geq 5$. We construct another eight "forbidden" grap…

According to the Tits conjecture proved by Crisp and Paris, [CP], the subgroups of the braid group generated by proper powers of the Artin elements are presented by the commutators of generators which are powers of commuting elements. Hence they are naturally presented as right-angled Artin groups. The case of subgroup…

We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. That is, if the right-angled Artin group G in Mod(S) satisfies certain conditions that imply G is quasi-isometrically embedded in Mod(S), then a purely pseudo-Anosov subgroup H of …

Study quasi-isometry invariants of square complexes and their applications.

We prove that every right-angled Artin group embeds into the $C^{\infty}$ diffeomorphism group of the real line. As a corollary, we show every limit group, and more generally every countable residually RAAG group, embeds into the $C^{\infty}$ diffeomorphism group of the real line.

We give a group theoretic characterization of geodesics with superlinear divergence in the Cayley graph of a right-angled Artin group A(G) with connected defining graph G. We use this to determine when two points in an asymptotic cone of A(G) are separated by a cut-point. As an application, we show that if G does not d…

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 braid group and into the area-preserving diffeomorphism groups of the 2--disk an…

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 complex of a right-angled Coxeter group. In the right-angled Artin group case it…

In this paper we consider several classical and novel algorithmic problems for right-angled Artin groups, some of which are closely related to graph theoretic problems, and study their computational complexity. We study these problems with a view towards applications to cryptography.

Extended characterization of RAAGs with zero minimal volume entropy.

We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group $A(Γ)$ fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups $\text{Mod}(S)$. In particular, such subgroups are quasiconvex in $A(Γ)$. In addition, we identify a milder cond…

Study shows shorter words for group elements in surface groups and RAAGs.

The paper extends arithmetic quotient results to right-angled Artin groups.

Homology growth of specific mapping tori vanishes for certain groups.

We construct an embedding of any right-angled Artin group $G(Δ)$ defined by a graph $Δ$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $Δ$. This construction yields an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid g…

Study of Dehn twists in free groups generates right-angled Artin groups.

New geometric spine for Artin groups defined by cube complexes.

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 products. In particular, for any irreducible right-angled Artin group we show that with …

We give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Moreover, we investigate the profinite topology of the direct product of two free groups. We show that the profinite topology of the above group is strongly connected wit…