相关论文: Local rigidity for actions of Kazhdan groups on no…

Let $\Gamma$ be a discrete group with property $(T)$ of Kazhdan. We prove that any Riemannian isometric action of $\Gamma$ on a compact manifold $X$ is locally rigid. We also prove a more general foliated version of this result. The…

We give a criterion for the rigidity of actions on homogeneous spaces. Let $G$ be a real Lie group, $\Lambda$ a lattice in $G$, and $\Gamma$ a subgroup of the affine group Aff$(G)$ stabilizing $\Lambda$. Then the action of $\Gamma$ on…

We study Popa's notion of rigidity for equivalence relations induced by actions on homogeneous spaces. For any lattices $\Gamma,\Lambda$ in a semisimple Lie group $G$ with finite center and no compact factors we prove that the action…

Let $J$ be a semisimple Lie group with all simple factors of real rank at least two. Let $\Gamma<J$ be a lattice. We prove a very general local rigidity result about actions of $J$ or $\Gamma$. This shows that almost all so-called "standard…

Motivated by Popa's seminal work \cite{Po04}, in this paper, we provide a fairly large class of examples of group actions $\Gamma \curvearrowright X$ satisfying the extended Neshveyev-St{\o}rmer rigidity phenomenon \cite{NS03}: whenever…

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 show that a discrete group $\Gamma$ which admits a non-elementary isometric action on a Hadamard manifold of bounded negative curvature admits an isometric action on an $L^p$-space $V$ for some $p>1$ with $H^1(\Gamma,V)\not=0$.

A locally compact group $G$ is a cocompact envelope of a group $\Gamma$ if $G$ contains a copy of $\Gamma$ as a discrete and cocompact subgroup. We study the problem that takes two finitely generated groups $\Gamma,\Lambda$ having a common…

We consider group measure space II$_1$ factors $M=L^{\infty}(X)\rtimes\Gamma$ arising from Bernoulli actions of ICC property (T) groups $\Gamma$ (more generally, of groups $\Gamma$ containing an infinite normal subgroup with relative…

Consider homogeneous G/H and G/F, for an S-algebraic group G. A lattice {\Gamma} acts on the left strictly conservatively. The following rigidity results are obtained: morphisms, factors and joinings defined apriori only in the measurable…

We show that, for a countable discrete group $\Gamma$, property $(\mathrm{T}_{L^p})$ of Bader, Furman, Gelander and Monod is equivalent to the property that, whenever an $L^p$-representation of $\Gamma$ admits a net of almost invariant unit…

In this article, we consider perturbations of isometries on a compact Riemannian manifold $M$. We investigate the smooth (resp. analytic) rigidity phenomenon of groups of these isometries. As a particular case, we prove that if a finite…

We show that if $\Gamma\curvearrowright (X^\Gamma,\mu^\Gamma)$ is a Bernoulli action of an i.c.c. nonamenable group $\Gamma$ which is weakly amenable with Cowling-Haagerup constant $1$, and $\Lambda\curvearrowright(Y,\nu)$ is a free ergodic…

It is well-known that a finitely generated group $\Gamma$ has Kazhdan's property (T) if and only if the Laplacian element $\Delta$ in ${\mathbb R}[\Gamma]$ has a spectral gap. In this paper, we prove that this phenomenon is witnessed in…

Let $G$ be a topological group with finite Kazhdan set, let $\Omega$ be a standard Borel space and $\mu$ a finite measure on $\Omega$. We prove that for any $p\in [1, \infty)$, any affine isometric action $G \curvearrowright L_p(\Omega,…

In this paper we study various rigidity aspects of the von Neumann algebra $L(\Gamma)$ where $\Gamma$ is a graph product group \cite{Gr90} whose underlying graph is a certain cycle of cliques and the vertex groups are the wreath-like…

Consider a countable group Gamma acting ergodically by measure preserving transformations on a probability space (X,mu), and let R_Gamma be the corresponding orbit equivalence relation on X. The following rigidity phenomenon is shown: there…

Let $G$ be the group of orientation-preserving isometries of a rank-one symmetric space $X$ of non-compact type. We study local rigidity of certain actions of a solvable subgroup $\Gamma \subset G$ on the boundary of $X$, which is…

Let $M$ be a finite volume analytic pseudo-Riemannian manifold that admits an isometric $G$-action with a dense orbit, where $G$ is a connected non-compact simple Lie group. For low-dimensional $M$, i.e. $\dim(M) < 2\dim(G)$, when the…

We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected…