相关论文: On the recognition of right-angled Artin groups

We use polyhedral product models to analyse the structure of the commutator subgroup of a right-angled Artin group. In particular, we provide a minimal set of generators for the commutator subgroup, consisting of special iterated…

We prove that, aside from the obvious exceptions, the mapping class group of a compact orientable surface is not abstractly commensurable with any right-angled Artin group. Our argument applies to various subgroups of the mapping class…

We describe the (co)homology of a certain family of normal subgroups of right-angled Artin groups that contain the commutator subgroup, as modules over the quotient group. We do so in terms of (skew) commutative algebra of squarefree…

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.

We prove that every right-angled Artin group occurs as a finite-index subgroup of the outer automorphism group of another right-angled Artin group. We furthermore show that the latter group can be chosen in such a way that the quotient is…

Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications.…

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.…

Twisted right-angled Artin groups are defined through presentation based on mixed graphs. Each vertex corresponds to a generator, each undirected edge yields a commuting relation and each directed edge gives a Klein bottle relation. If…

We explicitly construct an embedding of a right-angled Artin group into a classical pure braid group. Using this we obtain a number of corollaries describing embeddings of arbitrary Artin groups into right-angled Artin groups and linearly…

We determine which of the finite-type Artin groups are locally indicable, and compute presentations for their commutator subgroups.

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…

We prove that every finitely-generated right-angled Artin group can be embedded into some Brin-Thompson group $nV$. It follows that many other groups can be embedded into some $nV$ (e.g., any finite extension of any of Haglund and Wise's…

We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the…

For any right-angled Artin group, we show that its outer automorphism group contains either a finite-index nilpotent subgroup or a nonabelian free subgroup. This is a weak Tits alternative theorem. We find a criterion on the defining graph…

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…

Given a right-angled Artin group $G$ with finite outer automorphism group, we determine which right-angled Artin groups are measure equivalent (or orbit equivalent) to $G$.

We show that in any right-angled Artin group whose defining graph has chromatic number $k$, every non-trivial element has stable commutator length at least $1/(6k)$. Secondly, if the defining graph does not contain triangles, then every…

We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this remains undecidable among the fundamental groups of compact, non-positively curved square…

We compute the BNS-invariant for the pure symmetric automorphism groups of right-angled Artin groups. We use this calculation to show that the pure symmetric automorphism group of a right-angled Artin group is itself not a right-angled…

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…