相关论文: Automorphisms of two-dimensional right-angled Arti…

We define lines of minima in the thick part of Outer space for the free group Fn with n>2 generators. We show that these lines of minima are contracting for the Lipschitz metric. Every fully irreducible outer automorphism of Fn defines such…

Let G be a real semisimple Lie group with no compact factors and finite centre, and let $\Lambda$ be a lattice in G. Suppose that there exists a homomorphism from $\Lambda$ to the outer automorphism group of a right-angled Artin group…

For a locally compact metrizable group $G$, we consider the action of ${\rm Aut}(G)$ on ${\rm Sub}_G$, the space of all closed subgroups of $G$ endowed with the Chabauty topology. We study the structure of groups $G$ admitting automorphisms…

We give a bound for the virtually cyclic dimension of groups with a normal subgroup of finite index which satisfies that every infinite virtually-cyclic subgroup is contained in a unique maximal such subgroup. As an application we provide a…

We explore the existence of homomorphisms between outer automorphism groups of free groups Out(F_n) \to Out(F_m). We prove that if n > 8 is even and n \neq m \leq 2n, or n is odd and n \neq m \leq 2n - 2, then all such homomorphisms have…

Let $G$ be a countable group that splits as a free product of groups of the form $G=G_1\ast\dots\ast G_k\ast F_N$, where $F_N$ is a finitely generated free group. We identify the closure of the outer space…

We prove that $Out(F_N)$ is boundary amenable. This also holds more generally for $Out(G)$, where $G$ is either a toral relatively hyperbolic group or a finitely generated right-angled Artin group. As a consequence, all these groups satisfy…

This paper studies the geometric rigidity of the universal Coxeter group of rank $n$, which is the free product $W_n$ of $n$ copies of $\mathbb{Z}/2\mathbb{Z}$. We prove that for $n\geq 4$ the group of symmetries of the spine of the…

We prove that the full automorphism group and the outer automorphism group of the free group of countably infinite rank are coarsely bounded. That is, these groups admit no continuous actions on a metric space with unbounded orbits, and…

We study those fully irreducible outer automorphisms phi of a finite rank free group F_r which are ``parageometric'', meaning that the attracting fixed point of phi in the boundary of outer space is a geometric R-tree with respect to the…

We prove a rigidity result for cocycles from higher rank lattices to $\mathrm{Out}(F_N)$ and more generally to the outer automorphism group of a torsion-free hyperbolic group. More precisely, let $G$ be either a product of connected higher…

We compute the automorphism group of the intersection graph of many large-type Artin groups. This graph is an analogue of the curve graph of mapping class groups but in the context of Artin groups. As an application, we deduce a number of…

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…

We prove that all atoroidal automorphisms of $Out(F_N)$ act on the space of projectivized geodesic currents with generalized north-south dynamics. As an application, we produce new examples of non virtually cyclic, free and purely atoroidal…

The automorphisms of free groups with boundaries form a family of groups A_{n,k} closely related to mapping class groups, with the standard automorphisms of free groups as A_{n,0} and (essentially) the symmetric automorphisms of free groups…

For a large class of groups, we exhibit an infinite-dimensional space of homogeneous quasimorphisms that are invariant under the action of the automorphism group. This class includes non-elementary hyperbolic groups, infinitely-ended…

The well-rounded retract for $\mathrm{SL}_n(\mathbb{Z})$ is defined as the set of flat tori of unit volume and dimension $n$ whose systoles generate a finite-index subgroup in homology. This set forms an equivariant spine of minimal…

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…

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…

We prove that the outer automorphism group $\mathrm{Out}(N)$ of an infinitely generated free nilpotent group $N$ of class two is complete.