Related papers: Hyperbolic extensions of free groups

We consider the class $\mathcal{R}$ of finitely generated toral relatively hyperbolic groups. We show that groups from $\mathcal{R}$ are commutative transitive and generalize a theorem proved by Benjamin Baumslag to this class. We also…

Generalising results of Razborov and Safin, and answering a question of Button, we prove that for every hyperbolic group there exists a constant $\alpha >0$ such that for every finite subset $U$ that is not contained in a virtually cyclic…

Given an evolution algebra associated to a connected finite graph $\Gamma$, we exhibit a free action of the group of symmetries of $\Gamma$ on the set of automorphisms of the algebra. This allows us to explicitly describe this set and we…

We give a counterexample to a conjecture by Miasnikov, Ventura and Weil, stating that an extension of free groups is algebraic if and only if the corresponding morphism of their core graphs is onto, for every basis of the ambient group. In…

Let G be a graph of hyperbolic groups with 2-ended edge groups. We show that G is hierarchically hyperbolic if and only if G has no distorted infinite cyclic subgroup. More precisely, we show that G is hierarchically hyperbolic if and only…

We give upper bounds, linear in rank, to the topological dimensions of the Gromov boundaries of the intersection graph, the free factor graph and the cyclic splitting graph of a finitely generated free group.

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…

Let $G$ be a group acting acylindrically on a hyperbolic space and let $E$ be an exponential equation over $G$. We show that $E$ is equivalent to a finite disjunction of finite systems of pairwise independent equations which are either…

We find strictly ascending HNN extensions of finite rank free groups possessing a presentation 2-complex which is a non positively curved square complex. On showing these groups are word hyperbolic, we have by results of Wise and Agol that…

In this article, we state and prove a general criterion allowing us to show that some groups are hyperbolically elementary, meaning that every isometric action of one of these groups on a Gromov-hyperbolic space either fixes a point at…

We construct an example of a torsion free freely indecomposable finitely presented non-quasiconvex subgroup $H$ of a word hyperbolic group $G$ such that the limit set of $H$ is not the limit set of a quasiconvex subgroup of $G$. In…

We prove that non-elementary hyperbolic groups grow exponentially more quickly than their infinite index quasiconvex subgroups. The proof uses the classical tools of automatic structures and Perron-Frobenius theory. We also extend the main…

Let $N$ be a complete affine manifold $\mathbb{A}^n/\Gamma$ of dimension $n$, where $\Gamma$ is an affine transformation group acting on the complete affine space $\mathbb{A}^n$, and $K(\Gamma, 1)$ is realized as a finite CW-complex. $N$…

We Classify the rational quadratic extensions K and the finite groups G for which the group ring R[G] of G over the ring R of integers of K has the property that the group of units of augmentation 1 of R[G] is hyperbolic. We also construct…

A finitely presented, torsion free, abelian-by-cyclic group can always be written as an ascending HNN extension Gamma_M of Z^n, determined by an n x n integer matrix M with det(M) \ne 0. The group Gamma_M is polycyclic if and only if…

Let $N$ be a complete affine manifold $A^n/\Gamma$ of dimension $n$ where $\Gamma$ is an affine transformation group and $K(\Gamma, 1)$ is realized as a finite CW-complex. $N$ has a partially hyperbolic holonomy group if the tangent bundle…

We construct an uncountable sequence of groups acting uniformly properly on hyperbolic spaces. We show that only countably many of these groups can be virtually torsion-free. This gives new examples of groups acting uniformly properly on…

We prove an equivariant version of the fact that word-hyperbolic groups have finite asymptotic dimension. This is important in connection with our forthcoming proof of the Farrell-Jones conjecture in algebraic K-theory for every…

We refine Feighn--Handel's results on subgroups of mapping tori of free groups to the special case of free-by-cyclic groups. We use these refinements to show that any finitely generated free-by-cyclic group embeds in a {finitely generated…

A connected graph is called \emph{geodetic} if there is a unique geodesic between each pair of vertices. In this paper we prove that if a finitely generated group admits a Cayley graph which is geodetic, then the group must be virtually…