Related papers: On Properties of Expansive Group Actions

We establish a connection between two well-studied spaces of countable groups: the space of group operations and the space of marked groups. This connection shows that the two spaces are equivalent in terms of generic properties in the…

This paper introduces the concepts of correlation entropy and local correlation entropy for free semigroup actions on compact metric space, and explores their fundamental properties. Thereafter, we generalize some classical results on…

In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we propose definitions for definable actions and continuous…

We give a survey of various recent developments in orbit equivalence and measured group theory. This subject aims at studying infinite countable groups through their measure preserving actions.

The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.

The purpose of this paper is to study the action of the mapping class group on the moduli space of representations of the fundamental group of a non-orientable surface into SU(2). The action is shown to be ergodic with respect to a natural…

This is a (very subjective) survey paper for nonspecialists covering group actions on Gromov hyperbolic spaces. The first section is about hyperbolic groups themselves, while the rest of the paper focuses on mapping class groups and…

We develop a method of extending actions of compact transformation groups which is then applied to the problem of preservation of equivariant extensor property by passing to a subspace of given orbit types.

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 show that a non-expansive action of a topological semigroup S on a metric space X is linearizable iff its orbits are bounded. The crucial point here is to prove that X can be extended by adding a fixed point of S, thus allowing…

We extend the definition of algebraic entropy to endomorphisms of affine varieties. We calculate algebraic entropy of the action of elements of mapping class groups on various character varieties, and show that it is equal to a quantity we…

We present some results on reductions and the copolarity of isometric group actions, which we obtained in our thesis. We also describe a resolution construction for isometric actions with respect to a reduction and give examples.

We survey some results and questions about free actions of infinite groups on products of spheres and euclidean spaces, and give some new co-compact examples.

We introduce the concept of action space, a set $\boldsymbol{X}$ endowed with an action cost $\mathsf{a}:(0,+\infty)\times \boldsymbol{X}\times \boldsymbol{X}\to [0,+\infty)$ satisfying suitable axioms, which turn out to provide a `dynamic'…

Let a group $G$ act properly discontinuously and cocompactly on a locally compact space $X$. A Hausdorff compact space $Z$ that contains $X$ as an open subspace has the perspectivity property if the action $G\curvearrowright X$ extends to…

Let $(X, \cal B, \nu)$ be a probability space and let $\Gamma$ be a countable group of $\nu$-preserving invertible maps of $X$ into itself. To a probability measure $\mu$ on $\Gamma$ corresponds a random walk on $X$ with Markov operator $P$…

Let a compact Lie group act ergodically on a unital $C^*$-algebra $A$. We consider several ways of using this structure to define metrics on the state space of $A$. These ways involve length functions, norms on the Lie algebra, and Dirac…

The equivariant movability of topological spaces with an action of a given topological group $G$ is considered. In particular, the equivariant movability of topological groups is studied. It is proved that a second countable group $G$ is…

We present a general definition of entropy in the setting of pre-ordered semigroups, extending the notion of topological entropy. From our definition, we obtain the basic properties exhibited by various entropy-like theories encountered in…

The notions of quasiconvexity, Wright convexity and convexity for functions defined on a metric Abelian group are introduced. Various characterizations of such functions, the structural properties of the functions classes so obtained are…