Related papers: Extensions of Veech groups I: A hyperbolic action

Suppose G is a hyperbolic group whose boundary has topological dimension k. If the boundary is quasisymmetrically homeomorphic to an Ahlfors k-regular metric space, then, modulo a finite normal subgroup, G is isomorphic to a uniform lattice…

The end compactification |\Gamma| of the locally finite graph \Gamma is the union of the graph and its ends, endowed with a suitable topology. We show that \pi_1(|\Gamma|) embeds into a nonstandard free group with hyperfinitely many…

In this paper, we investigate finitely generated groups of isometries of CAT(0) spaces containing some central hyperbolic isometry, and study CAT(0) groups. We show that every CAT(0) group $\Gamma$ has the semi-direct product structure…

We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the…

We study surface groups $\Gamma$ in $SO(4,1)$, which is the group of Mobius tranformations of $S^3$, and also the group of isometries of $\mathbb{H}^4$. We consider such $\Gamma$ so that its limit set $\Lambda_\Gamma$ is a quasi-circle in…

We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly…

Let $\Gamma$ be the fundamental group of a closed orientable surface of genus at least two. Consider the composition of a uniformly random element of $\mathrm{Hom}(\Gamma,S_n)$ with the $(n-1)$-dimensional irreducible representation of…

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…

Let $(\Gamma,\mathbb{P})$ be a relatively hyperbolic group pair that is relatively one ended. Then the Bowditch boundary of $(\Gamma,\mathbb{P})$ is locally connected. Bowditch previously established this conclusion under the additional…

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…

This paper studies the locally uniform exponential growth and product set growth for a finitely generated group $G$ acting properly on a finite product of hyperbolic spaces. Under the assumption of coarsely dense orbits or shadowing…

Hierarchically hyperbolic spaces provide a common framework for studying mapping class groups of finite type surfaces, Teichm\"uller space, right-angled Artin groups, and many other cubical groups. Given such a space $\mathcal X$, we build…

We study complex hyperbolic disc bundles over closed orientable surfaces that arise from discrete and faithful representations H_n->PU(2,1), where H_n is the fundamental group of the orbifold S^2(2,...,2) and thus contains a surface group…

Let $\Gamma$ be a Schottky subgroup of $\mathrm{SL}_2(\mathbb{Z})$ and let $X=\Gamma\backslash \mathbb{H}^2$ be the associated hyperbolic surface. Conditional on the generalized Riemann hypothesis for quadratic $L$-functions, we establish a…

Let $G$ be the group of orientation-preserving isometries of a rank-one symmetric space $X$ of non-compact type. We study local rigidity of certain actions of a solvable subgroup $\Gamma \subset G$ on the boundary of $X$, which is…

We construct a nonuniform lattice and an infinite family of uniform lattices in the automorphism group of a hyperbolic building with all links a fixed finite building of rank 2 associated to a Chevalley group. We use complexes of groups and…

We study geometric properties of the action of the Picard modular group $\Gamma=PU(2,1,\mathcal{O}_7)$ on the complex hyperbolic plane $H^2_\mathbb{C}$, where $\mathcal{O}_7$ denotes the ring of algebraic integers in…

The classification of finite group-actions on closed surfaces of small genus is well-known. In the present paper we are interested in the question of which of these group-actions are bounding (extend to a compact 3-manifold with the surface…

Let $\mathcal{M}=\Gamma\backslash\mathbb{H}^{d+1}$ be a geometrically finite hyperbolic manifold with critical exponent exceeding $d/2$. We obtain a precise asymptotic expansion of the matrix coefficients for the geodesic flow in…

Let M be a Riemann surface with boundary $\partial M$ and genus greater than zero. Let $\Gamma$ be the mapping class group of M fixing $\partial M$. The group $\Gamma$ acts on ${\mathcal M}_{\mathcal C} = \Hom_{\mathcal…