Related papers: The minimum $b_2$ problem for right-angled Artin g…

We construct quasi-isometric embeddings from right-angled Artin groups into the outer automorphism group of a free group. These homomorphisms are in analogy with those constructed in \cite{CLM}, where the target group is the mapping class…

For each natural number $d$ we construct a $3$-generated group $H_d$, which is a subdirect product of free groups, such that the cohomological dimension of $H_d$ is $d$. Given a group $F$ and a normal subgroup $N \lhd F$ we prove that any…

In this article we study the right-angled Artin subgroups of a given right-angled Artin group. Starting with a graph $\gam$, we produce a new graph through a purely combinatorial procedure, and call it the extension graph $\gam^e$ of…

We construct "pushing maps" on the cube complexes that model right-angled Artin groups (RAAGs) in order to study filling problems in certain subsets of these cube complexes. We use radial pushing to obtain upper bounds on higher divergence…

We are motivated by the question that for which class of right-angled Artin groups (RAAG's), the quasi-isometry classification coincides with commensurability classification. This is previously known for RAAG's with finite outer…

Let $(M, g)$ be an $n$-dimensional complete Riemannian manifold with $Ric(M)\geq-(n-1)Q$, where $Q\geq0$ is a constant. We obtain an interior gradient bound for minimal graphs in $M\times R$ under some technical assumptions. For details,…

The Tits Conjecture, proved by Crisp and Paris, states that squares of the standard generators of any Artin group generate an obvious right-angled Artin subgroup. We consider a larger set of elements consisting of all the centers of the…

Let $\mathcal{C}$ be a class of finite groups closed under taking subgroups, quotients, and extensions with abelian kernel. The right-angled Artin pro-$\mathcal{C}$ group $G_\Gamma$ (pro-$\mathcal{C}$ RAAG for short) is the…

We show that for a sufficiently simple surface $S$, a right-angled Artin group $A(\Gamma)$ embeds into $\Mod(S)$ if and only if $\Gamma$ embeds into the curve graph $\mC(S)$ as an induced subgraph. When $S$ is sufficiently complicated,…

For the right-angled Artin group action on the extension graph, it is known that the minimal asymptotic translation length is bounded above by 2 provided that the defining graph has diameter at least 3. In this paper, we show that the same…

Let $p$ be a prime. The right-angled Artin pro-$p$ group $G_{\Gamma}$ associated to a fnite simplicial graph $\Gamma$ is the pro-$p$ completion of the right-angled Artin group associated to $\Gamma$. We prove that the following assertions…

Let $G$ be a right-angled Artin group with defining graph $\Gamma$ and let $H$ be a finitely generated group quasi-isometric to $G(\Gamma)$. We show if $G$ satisfies (1) its outer automorphism group is finite; (2) $\Gamma$ does not have…

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…

In 2018, M. Chu and S. Tillmann gave a lower bound for the trisection genus of a closed 4-manifold in terms of the Euler characteristic of $M$ and the rank of its fundamental group. We show that given a group $G$, there exist a 4-manifold…

In "Subgroups of Graph Groups", 1987, J. Alg., Droms proved that all the subgroups of a right-angled Artin group (RAAG) defined by a finite simplicial graph $\Gamma$ are themselves RAAGs if, and only if, $\Gamma$ has no induced square graph…

We study the outer automorphism group of a right-angled Artin group $A_\Gamma$ with finite defining graph $\Gamma$. We construct a subnormal series for $Out(A_\Gamma)$ such that each consecutive quotient is either finite, free-abelian,…

We demonstrate that the submonoid membership problem and the rational subset membership problem are equivalent in Artin groups. Both these problem are undecidable in a given Artin group if and only if the group embeds the right-angled Artin…

Let $\Gamma$ be a finite connected graph. The (unlabelled) configuration space $UC^n \Gamma$ of $n$ points on $\Gamma$ is the space of $n$-element subsets of $\Gamma$. The $n$-strand braid group of $\Gamma$, denoted $B_n\Gamma$, is the…

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…

Let $G$ be a right-angled Artin group with $|\mathrm{Out}(G)|<+\infty$. We prove that if a countable group $H$ with bounded torsion is measure equivalent to $G$, with an $L^1$-integrable measure equivalence cocycle towards $G$, then $H$ is…