Related papers: Group actions on metric spaces: fixed points and f…

We prove that the topological complexity of a finite index subgroup of a hyperbolic group is linear in its index. This follows from a more general result relating the size of the quotient of a free cocompact action of hyperbolic group on a…

We construct p.m.p. group actions that are not local-global limits of sequences of finite graphs. Moreover, they do not weakly contain any sequence of finite labeled graphs. Our methods are based on the study of almost automorphisms of…

This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…

We study the possible dimensions that the groups of holomorphic automorphisms of hyperbolic Reinhardt domains can have. We are particularly interested in the problem of characterizing Reinhardt domains with automorphism group of prescribed…

We give a general procedure for constructing metric spaces from systems of partitions. This generalises and provides analogues of Sageev's construction of dual CAT(0) cube complexes for the settings of hyperbolic and injective metric…

Four geometric conditions on a geodesic metric space, which are stronger variants of classical conditions characterizing hyperbolicity, are proved to be equivalent. In the particular case of the Cayley graph of a finitely generated group,…

Given any countable group $G$, we construct uncountably many quasi-isometry classes of proper geodesic metric spaces with quasi-isometry group isomorphic to $G$. Moreover, if the group $G$ is a hyperbolic group, the spaces we construct are…

We introduce a topometric version of Lipschitz-free spaces and study its universal property. Another aim of this paper is to investigate actions of topological groups $G$ on Lipschitz-free spaces $\mathcal{F}(M)$, induced by isometric…

The aim of this manuscript is to study some local properties of the topological entropy of a free semigroup action. In order to do that we focus on the set of entropy points of a free semigroup action, show that this set carries the full…

We generalize the notion of isoperimetric profiles of finitely generated groups to their actions by measuring the boundary of finite subgraphings of the orbit graphing. We prove that like the classical isoperimetric profiles for groups,…

In this article we prove that the set of torsion-free groups acting by isometries on a hyperbolic metric space whose entropy is bounded above and with a compact quotient is finite. The number of such groups can be estimated in terms of the…

Recall that a pseudofree group action on a space is one whose singular set consists only of isolated points. In this paper, we classify all of the finite groups which admit pseudofree actions on S^2 x S^2. The groups turn out to be exactly…

We present a careful approximation of the geodesics in trees of hyperbolic or relatively hyperbolic groups. As an application we prove a combination theorem for finite graphs of relatively hyperbolic groups, with both Farb's and Gromov's…

In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we…

Let $(M,\omega)$ be a connected symplectic manifold on which a connected Lie group $G$ acts properly and in a Hamiltonian fashion with moment map $\mu:M \lra \mf g^*$. Our purpose is investigate multiplicity-free actions, giving criteria to…

This paper is a survey of results proved in recent years that pertain to classifying cobounded hyperbolic actions of any group $G$. In other words, we discuss results that allow us to describe the partially ordered set $\mathcal{H}(G)$,…

In this paper we study chaotic behavior of actions of a countable discrete group acting on a compact metric space by self-homeomorphisms. For actions of a countable discrete group G, we introduce local weak mixing and Li-Yorke chaos; and…

We classify all group topologies coarser than the topology of stabilizers of finite sets in the case of automorphism groups of countable free-homogeneous structures, Urysohn space and Urysohn sphere, among other related results.

We survey rigidity results for groups acting on the circle in various settings, from local to global and $C^0$ to smooth. Our primary focus is on actions of surface groups, with the aim of introducing the reader to recent developments and…

In his 1985 paper Sullivan sketched a proof of his structural stability theorem for differentiable group actions satisfying certain expansion-hyperbolicity axioms. In this paper we relax Sullivan's axioms and introduce a notion of…