Related papers: On Almost Representations of Property (T) Groups

We define for discrete finitely presented groups a new property related to their asymptotic representations. Namely we say that a groups has the property AGA if every almost representation generates an asymptotic representation. We give…

Relative property (T) has recently been used to construct a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs…

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…

Let $G$ be a discrete group with property (T). It is a standard fact that, in a unitary representation of $G$ on a Hilbert space $\mathcal{H}$, almost invariant vectors are close to invariant vectors, in a quantitative way. We begin by…

In this article, we consider tensor products of unitary representations by irreducible non-unitary finite dimensional representations of topological groups to define a property that is a twisting of Kazhdan's Property (T). We use the…

Recently, a complete characterization of connected Lie groups with the Approximation Property was given. The proof used of the newly introduced property (T*). We present here a short proof of the same result avoiding the use of property…

We study Property (T) for locally compact quantum groups, providing several new characterisations, especially related to operator algebraic ergodic theory. Quantum Property (T) is described in terms of the existence of various Kazhdan type…

Kazhdan's property (T) has been studied for several discrete group-like structures, including standard invariants of Jones' subfactors and discrete quantum groups. We prove a Zuk-type spectral gap criterion for property (T) in this setting.…

We give a partial solution to a long-standing open problem in the theory of quantum groups, namely we prove that all finite-dimensional representations of a wide class of locally compact quantum groups factor through matrix quantum groups…

We introduce a notion of topological property (T) for \'etale groupoids. This simultaneously generalizes Kazhdan's property (T) for groups and geometric property (T) for coarse spaces. One main goal is to use this property (T) to prove the…

We prove that every sofic approximation of a property (T) group is approximately isomorphic to one having geometric property (T), and more generally, a box space of graphs which has boundary geometric property (T) is approximately…

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…

We study when the fiber product of groups with Property (T) has Property (T).

We prove that, for the free algebra over a sufficiently rich operad, a large subgroup of its group of tame automorphisms has Kazhdan's property (T). We deduce that there exists a group with property (T) that maps onto large powers of…

For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having…

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.

We prove that the notion of relative property (T) (or rigidity) for inclusions of finite von Neumann algebras defined in [Po1] is equivalent to a weaker property, in which no ``continuity constants'' are required. The proof is by…

For locally compact groups amenability and Kazhdan's property (T) are mutually exclusive in the sense that a group having both properties is compact. This is no longer true for more general Polish groups. However, a weaker result still…

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…

Every discrete group with Kazhdan's Property (T) is a quotient of a torsion-free, word hyperbolic group with Property (T).