Related papers: Property (T) for groups acting on affine buildings

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

We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the…

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…

We prove a local-to-global result for fixed points of groups acting on affine buildings (possibly non-discrete) of types $\tilde{A}_2$ or $\tilde{C}_2$. In the discrete case, our theorem establishes the corresponding special cases of a…

We show that if a group $G$ acts geometrically by type-preserving automorphisms on a building, then $G$ satisfies the weak Tits alternative, namely, that $G$ is either virtually abelian or contains a non-abelian free group.

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…

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…

We give a criterion of existence of a unipotent group action on the affine cone over a projective variety or, more generally, on the affine quasicone over a variety which is projective over another affine variety.

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…

Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite…

We study two transitivity properties for group actions on buildings, called Weyl transitivity and strong transitivity. Following hints by Tits, we give examples involving anisotropic algebraic groups to show that strong transitivity is…

Property (T) for groups means a dichotomy: a representation either has an invariant vector or all vectors are far from being invariant. We show that, under a stronger condition of A.Zuk, a similar dichotomy holds for almost representations…

We obtain a lifting property for finite quotients of algebraic groups, and applications to the structure of these groups.

We prove that the action of the automorphism group of a building on its boundary is topologically amenable. The notion of boundary we use was defined in a previous paper \cite{CL}. It follows from this result that such groups have property…

We use partial actions, as formalized by Exel, to construct various commensurating actions. We use this in the context of groups piecewise preserving a geometric structure, and we interpret the transfixing property of these commensurating…

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

We apply the Fixed Point Theorem for the actions of finite groups on Bruhat-Tits buildings and their products to establish two results concerning the groups of points of reductive algebraic groups over polynomial rings in one variable,…

We examine asymptotic dimension and property A for groups acting on complexes. In particular, we prove that the fundamental group of a finite, developable complex of groups will have finite asymptotic dimension provided the geometric…

We present some partial results concerning a-T-menability of groups acting on trees. Various known results are given uniform proofs.