Related papers: Well displacing representations and orbit maps

For a group $G$, let $U$ be the group of units of the integral group ring $\mathbb{Z}G$. The group $G$ is said to have the normalizer property if $\text{N}_U(G)=\text{Z}(U)G$. It is shown that Blackburn groups have the normalizer property.…

In this paper we further study links between concentration of measure in topological transformation groups, existence of fixed points, and Ramsey-type theorems for metric spaces. We prove that whenever the group $\Iso(\U)$ of isometries of…

We study a special class of graphs with a strong transience feature called uniform transience. We characterize uniform transience via a Feller-type property and via validity of an isoperimetric inequality. We then give a further…

We study isometric Lie group actions on symmetric spaces admitting a section, i.e. a submanifold which meets all orbits orthogonally at every intersection point. We classify such actions on the compact symmetric spaces with simple isometry…

Let $G$ be a metric group and let $\sA ut(G)$ denote the automorphism group of $G$. If $\sA$ and $\sB$ are groups of $G$-valued maps defined on the sets $X$ and $Y$, respectively, we say that $\sA$ and $\sB$ are \emph{equivalent} if there…

For a group acting on a hyperbolic space, we set up an algorithm in the group algebra showing that ideals generated by few elements are free, where few is a function of the minimal displacement of the action, and derive algebraic,…

Commability is the finest equivalence relation between locally compact groups such that $G$ and $H$ are equivalent whenever there is a continuous proper homomorphism $G \to H$ with cocompact image. Answering a question of Cornulier, we show…

We explore two properties of backward orbits under semigroups of holomorphic self-maps in the unit disk. First, we prove that regular backward orbits are quasi-geodesics for the hyperbolic distance of the unit disk. Then, we show that…

In this paper we study finite groups which have Cayley isomorphism property with respect to Cayley maps, CIM-groups for a brief. We show that the structure of the CIM-groups is very restricted. It is described in Theorem~\ref{111015a} where…

We define a numerical quasi-isometry invariant of a finitely generated group, whose values parametrize the difference between the group being uniformly embeddable in a Hilbert space and the reduced C*-algebra of the group being exact.

In this paper, we investigate certain graphs defined on groups, with a focus on infinite groups. The graphs discussed are the power graph, the enhanced power graph, and the commuting graph whose vertex set is a group $G$. The power graph is…

Given a separable metrisable space X, and a group G of homeomorphisms of X, we introduce a topological property of the action of G on X which is equivalent to the existence of a G-invariant compatible metric on X. This extends a result of…

Using tools from the theory of optimal transport, we establish several results concerning isometric actions of amenable topological groups with potentially unbounded orbits. Specifically, suppose $d$ is a compatible left-invariant metric on…

In this paper we define and investigate a class of groups characterized by a representation-theoretic property we call purely noncommuting or PNC. This property guarantees that the group has an action on a smooth projective variety with…

We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of…

Given a surface of higher genus, we will look at the Weil-Petersson completion of the Teichmuller space of the surface, and will study the isometric action of the mapping class group on it. The main observation is that the geometric…

Let $S$ be a closed oriented surface and $G$ a finite group of orientation preserving automorphisms of $S$ whose orbit space has genus at least $2$. There is a natural group homomorphism from the $G$-centralizer in $Diff^+(S)$ to the…

We show that if a group $G$ acts by isometries on a metric space $M$ which has asymptotic property C, such that the quasi-stabilizers of a point $x \in M$ have asymptotic dimension less than or equal to $n$, then $G$ itself has asymptotic…

Non-transitive subgroups of the orthogonal group play an important role in the non-Euclidean geometry. If $G$ is a closed subgroup in the orthogonal group such that the orbit of a single Euclidean unit vector does not cover the (Euclidean)…

In this paper, we study a special class of quasi-homomorphisms, i.e. quasi-retractions from a group to its subgroups. We first give some algebraic and geometric properties of quasi-retracts and then propose a theory of quasi-split short…