Related papers: Boundary of the Relative Outer Space

We characterize strongly Morse quasi-geodesics in Outer space as quasi-geodesics which project to quasi-geodesics in the free factor graph. We define convex cocompact subgroups of $Out(F_n)$ as subgroups such that an orbit map in the free…

For a finite group G of Lie type and a prime p, we compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic,…

We give elementary proofs of the following two theorems on automorphisms of a finite group G: (1) An automorphism of G is inner if and only if it extends to an automorphism of every finite group containing G. (2) There exists a finite…

In this paper we show that an affine space is determined by the abstract group structure of its group of regular automorphisms in the category of connected affine varieties. To prove this we study commutative subgroups of the group of…

Certain subgroups of the groups $Aut(F_n)$ of automorphisms of a free group $F_n$ are considered. Comparing Alexander polynomials of two poly-free groups $Cb_4^+$ and $P_4$ we prove that these groups are not isomorphic, despite the fact…

For any finitely generated group $G$, two complexity functions $\alpha_G$ and $\beta_G$ are defined to measure the maximal possible gap between the norm of an automorphism (respectively outer automorphism) of $G$ and the norm of its…

We prove central limit theorems for the random walks on either the mapping class group of a closed, connected, orientable, hyperbolic surface, or on $\text{Out}(F_N)$, each time under a finite second moment condition on the measure (either…

We prove that the group of outer automorphisms of the free Coxeter group $W_n$ is acylindrically hyperbolic in the sense of Osin. As an application, we observe that any CAT(0) space admitting a geometric action by Out($W_n$) must contain a…

Let $A=A(x_{1},...,x_{n})$ be a free associative algebra in $\mathcal{A}$ freely generated over $K$ by a set $X=\{x_{1},...,x_{n}\}$, $End A$ be the semigroup of endomorphisms of $A$, and $Aut End A$ be the group of automorphisms of the…

If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras and their ideals or subspaces. Varying the meaning of the…

The special linear groups, the mapping class groups of surfaces, the outer autormorphism groups of free groups appear in numerous domains. Their analogies, developped in particular in K. Vogtmann's work, have been written about a lot. In…

For every free product decomposition $G = G_{1} \ast ...\ast G_{q} \ast F_{r}$ of a group of finite Kurosh rank $G$, where $F_r$ is a finitely generated free group, we can associate some (relative) outer space $\mathcal{O}$. We study the…

It is shown that, modulo the automorphisms which fix the canonical diagonal MASA point-wise, the group of those automorphisms of the Cuntz algebra O_n which globally preserve both the diagonal and the core UHF-subalgebra is isomorphic, via…

We study the dilatation of outer automorphisms of right-angled Artin groups. Given a right-angled Artin group defined on a simplicial graph: $A(\Gamma) = \langle V | E \rangle$ and an automorphism $\phi \in Out(A(\Gamma))$ there is a…

A multiparameter quantum affine space of rank $n$ is the $\mathbb F$-algebra generated by indeterminates $X_1, \cdots, X_n$ satisfying $X_iX_j = q_{ij} X_jX_i \ (1 \le i < j \le n)$ where $q_{ij}$ are nonzero scalars in $\mathbb F^\ast$.…

It was previously shown by Grunewald and Lubotzky that the automorphism group of a free group, $\text{Aut}(F_n)$, has a large collection of virtual arithmetic quotients. Analogous results were proved for the mapping class group by Looijenga…

We study authomorphisms of $Ind$-groups of polynomial automorphisms (wich are singular) via tame approximations. Such objects were pioneeered in research by B.I.Plotkin We obtain a number of properties of $Aut(Aut(A))$, where $A$ is the…

We analyze the mapping class group of extendible automorphisms of the exterior boundary W of a compression body of dimension 3 or 4, which extend over the compression body (Q,V), where V is the interior boundary. Those that extend as…

Let $F(x, y)$ be a binary form of degree at least three and non-zero discriminant. In this article we compute the automorphism group $\operatorname{Aut} F$ for four families of binary forms. The first two families that we are interested in…

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…