Related papers: Distal actions and ergodic actions on compact grou…

To each totally disconnected, locally compact topological group G and each group A of automorphisms of G, a pseudo-metric space of ``directions'' has been associated by U. Baumgartner and the second author. Given a Lie group G over a local…

Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the…

Extending and unifying a number of well-known conjectures and open questions, we conjecture that locally elliptic (that is, every element has a bounded orbit) actions by automorphisms of finitely generated groups on finite dimensional…

Recently, Gareth Jones observed that every finite group $G$ can be realized as the group of automorphisms of some dessin d'enfant ${\mathcal D}$. In this paper, complementing Gareth's result, we prove that for every possible action of $G$…

In this paper, we extend the notion of temporo-spatial differentiation problems to the setting of actions of more general topological groups. The problem can be expressed as follows: Given an action $T$ of an amenable discrete group $G$ on…

This paper studies ergodic properties of certain measures arising in the dynamics of holomorphic correspondences. These measures, in general, are not invariant in the classical sense of ergodic theory. We define a notion of ergodicity, and…

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…

Let $\mathsf P$ be an operad acted upon by a group $G$, and let $\mathsf Q=\mathsf P\rtimes G$ be the corresponding framed operad. We relate the homotopy automorphism groups of $\mathsf P$ and $\mathsf Q$. We apply the result to compute the…

We extend Dye's reconstruction theorem, which classifies isomorphisms between full groups, to a classification of homomorphisms between full groups. For full groups of ergodic p.m.p. equivalence relations, our result roughly says that such…

This paper is a continuation of the authors' previous work on noncommutative joinings, and contains a study of relative independence of W$^*$-dynamical systems. We prove that, given any separable locally compact group $G$, an ergodic…

Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant geometric K-homology groups K^G_*(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural…

In a previous work, the second-named author gave a complete description of the action of automorphisms on the ordinary irreducible characters of the finite symplectic groups. We generalise this in two directions. Firstly, using work of the…

Local mean and individual (with respect to almost uniform convergence in Egorov's sense) ergodic theorems are established for actions of the semigroup $\mathbb R_+^d$ in symmetric spaces of measurable operators associated with a semifinite…

We define a random walk adic transformation associated to an aperiodic random walk on $G=\mathbb{Z}^{k}\times\mathbb{R}^{D-k}$ driven by a $\beta$-transformation and study its ergodic properties. In particular, this transformation is…

We describe the global structure of totally disconnected locally compact groups having a linear open compact subgroup. Among the applications, we show that if a non-discrete, compactly generated, topologically simple, totally disconnected…

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 study how the cohomology of nilpotent groups is affected by Lipschitz maps. We show that, given a smooth Lipschitz map $f$ between two simply-connected nilpotent Lie groups $G$ and $H$, there is a map $\psi$ that induces…

Let K be a fine hyperbolic graph and G be a group acting on K with finite quotient. We prove that G is exact provided that all vertex stabilizers are exact. In particular, a relatively hyperbolic group is exact if all its peripheral groups…

We describe the Segal $K$-theory of the symmetric monoidal category of finite-dimensional vector spaces over a perfect field $\mathbb{F}$ together with an automorphism, or, equivalently, the group-completion of the $E_\infty$-algebra of…

Given a countable abelian group $A$, we construct a row finite directed graph $\Gamma(A)$ such that the $K_{0}$-group of the graph $\textrm{C}^{\ast}$-algebra $\textrm{C}^{\ast}(\Gamma(A))$ is canonically isomorphic to $A$. Moreover, each…