Related papers: Cocycle Superrigidity for Profinite Actions of Pro…

We prove the first orbit equivalence superrigidity results for actions of type III$_\lambda$ when $\lambda \neq 1$. These actions arise as skew products of actions of dense subgroups of $SL(n,\mathbb{R})$ on the sphere $S^{n-1}$ and they…

Let $\Gamma$ be a finitely generated group which admits an action by homeomorphisms on a compact metrizable space $X$. We show that there is a metric on $X$ defining the original topology such that for this metric, the action is by…

We revisit Margulis-Zimmer Super-Rigidity and provide some generalizations. In particular we obtain super-rigidity results for lattices in higher-rank groups or product of groups, targeting at algebraic groups over arbitrary fields with…

This paper deals with the extension of partial actions of topological groups on topological spaces. Within this framework, we introduce a class of topological embeddings defined via the inverse semigroup of homeomorphisms between open…

Let $\Gamma$ be a finitely generated group and let $(X,\mu_X)$ be an ergodic standard Borel probability $\Gamma$-space. Suppose that $G$ is the connected component of the identity of the isometry group of a Hermitian symmetric space. Given…

Following the work of Burger, Iozzi and Wienhard for representations, in this paper we introduce the notion of maximal measurable cocycles of a surface group. More precisely, let $\mathbf{G}$ be a semisimple algebraic $\mathbb{R}$-group…

Let $G$ be a right-angled Artin group with $|\mathrm{Out}(G)|<+\infty$. We prove that if a countable group $H$ with bounded torsion is measure equivalent to $G$, with an $L^1$-integrable measure equivalence cocycle towards $G$, then $H$ is…

Suppose a locally compact group G acts freely and properly on a locally compact Hausdorff space X, and let gamma be the induced action on C_0(X). We consider a category in which the objects are C*-dynamical systems (A, G, alpha) for which…

Let $X$ be a locally finite irreducible affine building of dimension $\geq 2$ and $\Gamma \leq \mathrm{Aut}(X)$ be a discrete group acting cocompactly. The goal of this paper is to address the following question: When is $\Gamma$ linear?…

We say that two free probability-measure-preserving actions of countable groups are Shannon orbit equivalent if there is an orbit equivalence between them whose associated cocycle partitions have finite Shannon entropy. We show that if the…

A countable group \Gamma is called shift-minimal if every non-trivial measure preserving action of \Gamma weakly contained in the Bernoulli shift of \Gamma on ([0,1]^\Gamma ,\lambda ^\Gamma) is free. We show that any group \Gamma whose…

If $G$ is a complex simply connected semisimple algebraic group and if $\lambda$ is a dominant weight, we consider the compactification $X_\lambda$ in the projectivisation of $\End(V(\lambda))$ obtained as the closure of the $G\times…

We give a proof, based on thermodynamic formalism, of a theorem in bounded cohomology extending a foundational result of Burger and Monod: if $\Gamma$ is an irreducible uniform lattice in a non-compact connected semisimple Lie group of real…

We complement the characterization of the graph products of cyclic groups $G(\Gamma, \mathfrak{p})$ admitting a Polish group topology of [9] with the following result. Let $G = G(\Gamma, \mathfrak{p})$, then the following are equivalent:…

We study the cohomology of families of $(\varphi,\Gamma)$-modules with coefficients in pseudoaffinoid algebras. We prove that they have finite cohomology, and we deduce an Euler characteristic formula and Tate local duality. We classify…

We consider skew products $$T_\phi:X\times G\to X\times G,~~(x,g)\mapsto(F_1(x),g\;\!\phi(x)),$$ where $X$ is a compact manifold with probability measure, $G$ a compact Lie group with Lie algebra $\frak g$, $F_1:X\to X$ the time-one map of…

Answering a question by Chatterji--Dru\c{t}u--Haglund, we prove that, for every locally compact group $G$, there exists a critical constant $p_G \in [0,\infty]$ such that $G$ admits a continuous affine isometric action on an $L_p$ space…

We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely generated groups. These groups are of the form $\Gamma…

These notes contain an Ergodic-theoretic account of the Cocycle Superrigidity Theorem recently discovered by Sorin Popa. We state and prove a relative version of the result, discuss some applications to measurable equivalence relations, and…

Every homomorphism from finite index subgroups of a universal lattices to mapping class groups of orientable surfaces (possibly with punctures), or to outer automorphism groups of finitely generated nonabelian free groups must have finite…