Related papers: Fractional distortion in hyperbolic groups

Sela proved every torsion-free one-ended hyperbolic group is coHopfian. We prove that there exist torsion-free one-ended hyperbolic groups that are not commensurably coHopfian. In particular, we show that the fundamental group of every…

The computational complexity of the word problem in HNN-extension of groups is studied. HNN-extension is a fundamental construction in combinatorial group theory. It is shown that the word problem for an ascending HNN-extension of a group H…

The goal of the article is to prove that four explicitly given transformations, two Heisenberg translations, a rotation and an involution generate the Picard modular group with Gaussian integers acting on the two dimensional complex…

This paper proves under certain conditions the existence of an algorithm, which detects relatively quasiconvex subgroups $H$ of relatively hyperbolic groups $(G,\mathbb{P})$. Additionally, this algorithm outputs an induced peripheral…

Let $K$ be a non-cylotomic imaginary quadratic field of class number 1 and $E/K$ is an elliptic curve with $E(K)[2]\simeq \mathbb{Z}/2\mathbb{Z} \oplus\mathbb{Z}/2\mathbb{Z}.$ In this article, we determine the torsion groups that can arise…

Let $G$ be a split connected reductive group over a finite extension $F$ of $Q_p$. We determine the extensions between unitary continuous $p$-adic and smooth mod $p$ principal series of $G(F)$ in the generic case. In order to do so, we…

In this article we characterize the complex hyperbolic groups that leave invariant a copy of the Veronese curve in $\Bbb{P}^2_{\Bbb{C}}$. As a corollary we get that every discrete compact surface group in $\PO^+(2,1)$ admits a deformation…

If a torsion-free hyperbolic group G has 1-dimensional boundary, then the boundary is a Menger curve or a Sierpinski carpet provided G does not split over a cyclic group. When the boundary of G is a Sierpinski carpet we show that G is a…

We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite dimensional CAT(0)-space.

We explicitly construct a dynamically incoherent partially hyperbolic endomorphisms of $\mathbb{T}^2$ in the homotopy class of any linear expanding map with integer eigenvalues. These examples exhibit branching of centre curves along…

A morphism of linear algebraic groups $\phi:K\rightarrow G$ is called an epimorphism if it admits right cancellation. A subgroup $H\leq G$ is epimorphic if the inclusion map is an epimorphism. For $G$ a simple algebraic group over an…

We determine, for an elliptic curve $E/\mathbb Q$ and for all $p$, all the possible torsion groups $E(\mathbb Q_{\infty, p})_{tors}$, where $\mathbb Q_{\infty, p}$ is the $\mathbb Z_p$-extension of $\mathbb Q$.

A family of deformed Hopf algebras corresponding to the classical maximal isometry algebras of zero-curvature N-dimensional spaces (the inhomogeneous algebras iso(p,q), p+q=N, as well as some of their contractions) are shown to have a…

An open question asks whether every group acting acylindrically on a hyperbolic space has uniform exponential growth. We prove that the class of groups of uniform uniform exponential growth acting acylindrically on a hyperbolic space is…

We initiate the study of deformations of groups in three-dimensional complex hyperbolic geometry. Let $$G=\left\langle \iota_1, \iota_2, \iota_3, \iota_4 \Bigg| \begin{array}{c} \iota_1^2= \iota_2^2 = \iota_3^2=\iota_4^2=id,\\ (\iota_1…

The hyperlinear profile of a group measures the growth rate of the dimension of unitary approximations to the group. We construct a finitely-presented group whose hyperlinear profile is at least subexponential, i.e. at least…

Given a periodic quotient of a torsion-free hyperbolic group, we provide a fine lower estimate of the growth function of any sub-semi-group. This generalizes results of Razborov and Safin for free groups.

We study to what extent torsion-free (Gromov)-hyperbolic groups are elementarily equivalent to their finite index subgroups. In particular, we prove that a hyperbolic limit group either is a free product of cyclic groups and surface groups,…

Let $ M$ be a cusped hyperbolic $ 3$-manifold, e.g. a knot complement. Thurston showed that the space of deformations of its fundamental group in $ \mathrm {PGL}(2,\mathbf {C})$ (up to conjugation) is of complex dimension the number $ \nu $…

We study automorphisms of a relatively hyperbolic group G. When G is one-ended, we describe Out(G) using a preferred JSJ tree over subgroups that are virtually cyclic or parabolic. In particular, when G is toral relatively hyperbolic,…