Related papers: Relative Property (T) and Linear Groups

We define a relative property A for a countable group with respect to a finite family of subgroups. Many characterizations for relative property A are given. In particular a relative bounded cohomological characterization shows that if a…

In this paper we continue the investigation of a real number object, i.e., an object representing the real numbers, in categories of relations. Our axiomatization is based on a relation algebraic version of Tarski's axioms of the real…

Let p be a real number with 1<p and different from 2. We study Property (T_lp) for a second countable locally compact group G. Property (T_lp) is a weak version of Kazhdan's Property (T), defined in terms of the orthogonal representations…

We introduce the notion of L^2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that…

This paper discusses `geometric property (T)'. This is a property of metric spaces introduced in earlier work of the authors for its applications to K-theory. Geometric property (T) is a strong form of `expansion property': in particular…

In this note, we will point out, as a corollary of Popa's rigidity theory, that the crossed product von Neumann algebras for Bernoulli shifts cannot have relative property T. This is an operator algebra analogue of the theorem shown by…

The notion of strong 1-boundedness for finite von Neumann algebras was introduced by Jung in arXiv:math/0510576 . This framework provided a free probabilistic approach to study rigidity properties and classification of finite von Neumann…

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…

Property $(TTT)$ was introduced by Ozawa as a strengthening of Kazhdan's property $(T)$ and Burger and Monod's property $(TT)$. In this paper, we improve Ozawa's result by showing that any simple algebraic group of rank $\geq 2$ over a…

We prove that a group acting geometrically on a thick affine building has property (T). A more general criterion for property (T) is given for groups acting on partite complexes.

Using a m\'elange of techniques at the rich intersection of deformation/rigidity theory, finite index subfactor theory, and geometric group theory, we prove the existence of a continuum of property (T) factors that are pairwise non-stably…

We introduce a notion of shadowing property for actions of finitely generated groups and study its basic properties. We formulate and prove a shadowing lemma for actions of nilpotent groups. We construct an example of a faithful linear…

We give a complete characterization of connected Lie groups with the Approximation Property for groups (AP). To this end, we introduce a strengthening of property (T), that we call property (T*), which is a natural obstruction to the AP. In…

A countable discrete group $\Gamma$ is said to have the relative ISR-property if for every non-trivial normal subgroup $N\trianglelefteq\Gamma$ and every von Neumann subalgebra $\mathcal{M}\subseteq L(\Gamma)$ invariant under conjugation by…

We say that a group has property $R_{\infty}$ if any group automorphism has an infinite number of twisted conjugacy classes. Fel'shtyn and Goncalves prove that the solvable Baumslag-Solitar groups BS(1,m) have property $R_{\infty}$. We…

Let $H$ be a proper subgroup of a discrete group $G$. We introduce a notion of relative inner amenability of $H$ in $G$, we prove some equivalent conditions and provide examples as well as counter-examples. We also discuss the corresponding…

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 $G$ be a non-compact semisimple Lie group with finite centre and finitely many components. We show that any finitely generated group $\Gamma$ which is quasi-isometric to an irreducible lattice in $G$ has the $R_\infty$-property, namely,…

In this article we study property (T) groups arising from Rips construction in geometric group theory in the spirit of \cite{CDK19} and certain inductive limit groups from this class. Using interplay between Popa's deformation/rigidity and…

D. A. Kahzdan first put forth property (T) in relation to the study of discrete subgroups of Lie groups of finite co-volume. Through a combinatorial approach, we define an analogue of property (T) for regular graphs. We then prove the basic…