Related papers: Topological property (T) for groupoids

We propose a description of T-duality between general geometric and non-geometric backgrounds as higher groupoid bundles with connections. Our description extends the previous observation by Nikolaus and Waldorf that the topological aspects…

The aim of this partly expository paper is to present and discuss two classes of sets of integers (Jamison and Kazhdan sets) whose definition and/or properties are determined or inspired by operator-theoretical properties. Jamison sets…

For any type of fundamental groupoid scheme, we construct an algebraic cohomology theory for varieties with coefficients in the base field. This is a minor variant of \'etale cohomology, involving neither de Rham complexes nor…

In this paper, we provide several instances in which interesting approximation and stability properties are inherited by quotients with respect to finitely generated normal subgroups or, more strongly, normal subgroups with Kazhdan's…

Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the K-groups of the (reduced) groupoid C*-algebra, provided the groupoid has torsion-free…

We show an analogue of Jordan's theorem for algebraic groups defined over a field $\mathbb k$ of arbitrary characteristic. As a consequence, a Jordan-type property holds for the automorphism group of any projective variety over $\mathbb k$.

We present a recent result of Ibarluc\'ia stating that every Roelcke precompact Polish group has Kazhdan's property (T). This striking theorem builds on the characterization of Roelcke precompact Polish groups as automorphism groups of…

In this paper, we introduce quotients of \'etale groupoids. Using the notion of quotients, we describe the abelianizations of groupoid C*-algebras. As another application, we obtain a simple proof that effectiveness of an \'etale groupoid…

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…

The main goal of this paper is to prove that every Golod-Shafarevich group has an infinite quotient with Kazhdan's property $(T)$. In particular, this gives an affirmative answer to the well-known question about non-amenability of…

D. Kazhdan has introduced in 1967 the Property (T) for local compact groups. In this article we prove that for $n\geq 3$ and $m \in \mathbb{N}$ the group $SL_n(\textbf{K})\ltimes \mathcal{M}_{n,m}(\textbf{K})$ is a Kazhdan group having the…

We survey the recent developments concerning fixed point properties for group actions on Banach spaces. In the setting of Hilbert spaces such fixed point properties correspond to Kazhdan's property (T). Here we focus on the general,…

We show that groupoid equivalence preserves a number of groupoid properties such as properness or the property of being topologically principal.

We construct first examples of infinite groups having property (T) whose Kazhdan constants admit a lower bound independent of the choice of a finite generating set.

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

In this paper, we propose a property which is a natural generalization of Kazhdan's property $(T)$ and prove that many, but not all, groups with property $(T)$ also have this property. Let $\G$ be a finitely generated group. One definition…

For any topological group $G$ the dual object $\hat G$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\hat G$ is discrete, and we investigate…

We characterize the situations in which certain accumulation properties of topological spaces are preserved under taking products.

We establish a fixed point property for a certain class of locally compact groups, including almost connected Lie groups and compact groups of finite abelian width, which act by simplicial isometries on finite rank buildings with measurable…

We study Bowditch's notion of a coarse median on a metric space and formally introduce the concept of a coarse median structure as an equivalence class of coarse medians up to closeness. We show that a group which possesses a uniformly…