Related papers: Type VF for outer automorphism groups of large-typ…

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 construct the first known examples of infinite subgroups of the outer automorphism group of Out(A_Gamma), for certain right-angled Artin groups A_Gamma. This is achieved by introducing a new class of graphs, called focused graphs, whose…

For a right-angled Artin group $A_\Gamma$, the untwisted outer automorphism group $U(A_\Gamma)$ is the subgroup of $Out(A_\Gamma)$ generated by all of the Laurence-Servatius generators except twists (where a {\em twist} is an automorphisms…

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…

For any right-angled Artin group $A_{\Gamma}$ we construct a finite-dimensional space $\mathcal{O}_{\Gamma}$ on which the group $\text{Out}(A_{\Gamma})$ of outer automorphisms of $A_{\Gamma}$ acts with finite point stabilizers. We prove…

We study the acylindrical hyperbolicity of the outer automorphism group of a right-angled Artin group $A_\Gamma$. When the defining graph $\Gamma$ has no SIL-pair (separating intersection of links), we obtain a necessary and sufficient…

For any right-angled Artin group $A_{\Gamma}$, Charney--Stambaugh--Vogtmann showed that the subgroup $U^0(A_{\Gamma}) \leq\text{Out}(A_{\Gamma})$ generated by Whitehead automorphisms and inversions acts properly and cocompactly on a…

We show that the twisted conjugacy problem is solvable for large-type Artin groups whose outer automorphism group is finite, generated by graph automorphisms and the global inversion. This includes XXXL Artin groups whose defining graph is…

In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by…

Using the canonical JSJ splitting, we describe the outer automorphism group $\Out(G)$ of a one-ended word hyperbolic group $G$. In particular, we discuss to what extent $\Out(G)$ is virtually a direct product of mapping class groups and a…

For G, H two finite collections of finitely generated subgroups of a right-angled Artin group A, the untwisted McCool group U(A; G, Ht) is the subgroup of untwisted outer automorphisms of A preserving the conjugacy class of each element of…

We define the symmetric (outer) automorphism group of a right-angled Artin group and construct for it a (spine of) Outer space. This `symmetric spine' is a contractible cube complex upon which the symmetric outer automorphism group acts…

Outer automorphism groups of RAAGs, denoted $Out(A_\Gamma)$, interpolate between $Out(F_n)$ and $GL_n(\mathbb{Z})$. We consider several vastness properties for which $Out(F_n)$ behaves very differently from $GL_n(\mathbb{Z})$: virtually…

We study fixed subgroups of automorphisms of any large-type Artin group $A_{\Gamma}$. We define a natural subgroup $\mathrm{Aut}_\Gamma(A_\Gamma)$ of $\mathrm{Aut}(A_{\Gamma})$, and for every $\gamma \in \mathrm{Aut}_\Gamma(A_\Gamma)$ we…

The virtual cohomological dimension of~$\operatorname{Out}(F_n)$ is given precisely by the dimension of the spine of Culler--Vogtmann Outer space. However, the dimension of the spine of untwisted Outer space for a general right-angled Artin…

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…

We compute explicitly the automorphism and outer automorphism group of all large-type free-of-infinity Artin groups. Our strategy involves reconstructing the associated Deligne complexes in a purely algebraic manner, i.e. in a way that is…

In this paper we study Sigma invariants of even Artin groups of FC-type, extending some known results for right-angled Artin groups. In particular, we define a condition that we call the strong homological $n$-link condition for a graph…

We give a condition on the defining graph of a right-angled Artin group which implies its automorphism group is virtually indicable, that is, it has a finite-index subgroup that admits a homomorphism onto $\Z$. We use this as part of a…

For a classical group $G$ of type $\mathsf D_n$ over a field $k$ of characteristic different from $2$, we show the existence of a finitely generated regular extension $R$ of $k$ such that $G$ admits outer automorphisms over $R$. Using this…