Related papers: New spectral multiplicities for ergodic actions

We consider a new orbit equivalence invariant for measure-preserving actions of groups on the probability space, $\sigma:G\to$ Aut$(X,\mu)$, denoted $\chi_0(\sigma;G)$ and defined as the "intersection" of the 1-cohomology group,…

In this paper we show that for every congruent monotileable amenable group $G$ and for every metrizable Choquet simplex $K$, there exists a minimal $G$-subshift, which is free on a full measure set, whose set of invariant probability…

We prove that locally countably-compact Hausdorff topological groups $\mathbb{G}$ act continuously on their iterated joins $E_n\mathbb{G}:=\mathbb{G}^{*(n+1)}$ (the total spaces of the Milnor-model $n$-universal $\mathbb{G}$-bundles) as…

We solve the question of the existence of a Poisson-Pinsker factor for conservative ergodic infinite measure preserving action of a countable amenable group by proving the following dichotomy: either it has totally positive Poisson entropy…

A probability measure preserving action of \Gamma on (X,\mu) is called rigid if the inclusion of L^\infty(X) into the crossed product L^\infty(X) \rtimes \Gamma has the relative property (T) in the sense of Popa. We give examples of rigid,…

Let G be an orthogonal or symplectic p-adic group (not necessarily split) or an inner form of a general linear p-adic group. In a previous paper, it was shown that the Bernstein components of the category of smooth representations of G are…

We give a systematic presentation of the stability theory in the non-algebraic Kaehlerian geometry. We introduce the concept of "energy complete Hamiltonian action". To an energy complete Hamiltonian action of a reductive group G on a…

We continue our study of when topological and measure-theoretic entropy agree for algebraic action of sofic groups. Specifically, we provide a new abstract method to prove that an algebraic action is strongly sofic. The method is based on…

Following methods of Bannon-Marrakchi-Ozawa, we show that for coamenable inclusion $\mathcal{S}\leq \mathcal{R}$ of ergodic, probability measure-preserving relations, we have that $\mathcal{R}$ is strongly ergodic if and only if…

We present: 1) a mixing $Z ^ 2$-action with the following asymmetry of multiple mixing property: for some commuting measure-preserving transformations $S$, $T$ and a sequence $n_j$ $$ \lim_{j\to \infty}\mu(A\bigcap S^{-n_j}A\bigcap…

We show that given any subgroup F of R_+ which is either countable or belongs to a certain "large" class of uncountable subgroups, there exist continuously many free ergodic probability measure preserving actions \sigma_i of the free group…

Let $G$ be a countable group and $X$ be a totally regular curve. Suppose that $\phi:G\rightarrow {\rm Homeo}(X)$ is a minimal action. Then we show an alternative: either the action is topologically conjugate to isometries on the circle…

Let $\eta$ be an arbitrary countable ordinal. Using results of Bourgain and Gamburd on compact systems with spectral gap we show the existence of an action of the free group on three generators $F_3$ on a compact metric space $X$, admitting…

Suppose that $G$ is a locally compact group and $\pi$ is a (not necessarily irreducible) unitary representation of a closed normal subgroup $N$ of $G$ on a Hilbert space $H$. We extend results of Clifford and Mackey to determine when $\pi$…

To any trace preserving action $\sigma: G \curvearrowright A$ of a countable discrete group on a finite von Neumann algebra $A$ and any orthogonal representation $\pi:G \to \mathcal O(\ell^2_{\mathbb{R}}(G))$, we associate the generalized…

We introduce and study various notions of amenability continuous (Borel) partial actions of locally compact (Borel) groups $G$ on topological (standard Borel) spaces. We also study amenability of partial representations of a locally compact…

In this short note we study the entropy for algebraic actions of certain amenable groups. The possible values for this entropy are studied. Various fundamental results about certain classes of amenable groups are reproved using elementary…

Let $G$ be a real semisimple Lie group with finite centre and without compact factors, $Q<G$ a parabolic subgroup and $X$ a homogeneous space of $G$ admitting an equivariant projection on the flag variety $G/Q$ with fibres given by copies…

Given a unitary representation $U$ of an Abelian group $G$ and a subgroup $H$, we characterise the positive operator valued quotient group $G/H$ and covariant with respect to $U$.

A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1]…