相关论文: Automorphism and outer automorphism groups of Righ…

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, 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…

We study atomic right-angled Artin groups -- those whose defining graph has no cycles of length less than five, and no separating vertices, separating edges, or separating vertex stars. We show that these groups are not quasi-isometrically…

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…

We show that there is no uniform upper bound on |Out(Aut(A))| when A ranges over all right-angled Artin groups. This is in contrast with the cases where A is free or free abelian: for all n, Dyer-Formanek and Bridson-Vogtmann showed that…

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 prove that the separating curve graph of a connected, compact, orientable surface with genus at least 3 and a single boundary component is not relatively hyperbolic. This completes the classification of when the separating curve graph is…

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 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…

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…

An automorphism $\alpha$ of a group $G$ is normal if it fixes every normal subgroup of $G$ setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively…

We prove that the outer automorphism group of a one-ended hyperbolic group is virtually a hierarchically hyperbolic group (HHG), under mild orientability conditions on the associated JSJ decomposition. This is done by proving that a…

This article is dedicated to the study of the acylindrical hyperbolicity of automorphism groups of graph products of groups. Our main result is that, if $\Gamma$ is a finite graph which contains at least two vertices and is not a join and…

In this paper we study the hyperbolicity properties of a class of random groups arising as graph products associated to random graphs. Recall, that the construction of a graph product is a generalization of the constructions of right-angled…

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…

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 study the automorphisms of graph products of cyclic groups, a class of groups that includes all right-angled Coxeter and right-angled Artin groups. We show that the group of automorphism generated by partial conjugations is itself a…

We prove that if two transvection-free right-angled Artin groups are measure equivalent, then they have isomorphic extension graphs. As a consequence, two right-angled Artin groups with finite outer automorphism groups are measure…

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 show that one can define and effectively compute Stallings graphs for quasi-convex subgroups of automatic groups (\textit{e.g.} hyperbolic groups or right-angled Artin groups). These Stallings graphs are finite labeled graphs, which are…