Related papers: Relative Kazhdan Property

A compact Lie group G and a faithful complex representation V determine a Sato-Tate measure, defined as the direct image of Haar measure on G with respect to the character of V. We give a necessary and sufficient condition for a Sato-Tate…

We are mainly interested here in Kazhdan's property T for measured equivalence relations. Among our main results are characterizations of strong ergodicity and Kazhdan's property in terms of the spectra of diffusion operators, associated to…

In 1993, Lubotzky and Weiss conjectured that if a compact group admits two finitely generated dense subgroups, one of which is amenable and the other has Kazhdan's property (T), then it would be finite. This conjecture was resolved in the…

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…

Pseudo-automorphisms are birational transformations acting as regular automorphisms in codimension 1. We import ideas from geometric group theory to prove that a group of birational transformations that satisfies a fixed point property on…

Fix an integral semisimple element $\lambda$ in the Lie algebra $\mathfrak{g}$ of a complex reductive algebraic group $G$. Let $L$ denote the centralizer of $\lambda$ in $G$ and let $\mathfrak{g}(-1)$ denote the $-1$ eigenspace of…

Special matchings are purely combinatorial objects associated with a partially ordered set, which have applications in Coxeter group theory. We provide an explicit characterization and a complete classification of all special matchings of…

We explain, following Gromov, how to produce uniform isometric actions of groups starting from isometric actions without fixed point, using common ultralimits techniques. This gives in particular a simple proof of a result by Shalom:…

We investigate the padded version of reduction, an extension of multifraction reduction as defined in arXiv:1606.08991, and connect it both with ordinary reduction and with the so-called Property $\mathrm{H}$. As an application, we show…

Let a compact group G act on real or complex C*-algebras A and B, with A separable and B sigma-unital. We express the G-equivariant Kasparov groups KK_n(A,B) by algebraic K-groups of a certain additive category.

The well-known theorem of Shalom--Vaserstein and Ershov--Jaikin-Zapirain states that the group $\mathrm{EL}_n(\mathcal{R})$, generated by elementary matrices over a finitely generated commutative ring $\mathcal{R}$, has Kazhdan's property…

We investigate the properties of relative analogues of admissible Ind, Pro, and elementary Tate objects for pairs of exact categories, and give criteria for those categories to be abelian. A relative index map is introduced, and as an…

In the first part of the work (Sections 2-6) a special attention is given to relative separation axioms and relative connectedness, in particular, many relative versions of p-T_0, p-T_1, p-T_2, (i,j)- and p-regularities, (i,j)- and…

We introduce and study relatively divisible and relatively flat objects in exact categories in the sense of Quillen. For every relative cotorsion pair $(\mathcal{A},\mathcal{B})$ in an exact category $\mathcal{C}$, $\mathcal{A}$ coincides…

Kazhdan constants of discrete groups are hard to compute and the actual constants are known only for several classes of groups. By solving a semidefinite programming problem by a computer, we obtain a lower bound of the Kazhdan constant of…

In 2010, Invent. Math., Ershov and Jaikin-Zapirain proved Kazhdan's property (T) for elementary groups. This expository article focuses on presenting an alternative simpler proof of that. Unlike the original one, our proof supplies no…

For a pair of spaces $X$ and $Y$ such that $Y \subseteq X$, we define the relative topological complexity of the pair $(X,Y)$ as a new variant of relative topological complexity. Intuitively, this corresponds to counting the smallest number…

Assume that $\mathcal{P}$ is a topological property of a space $X$, then we say that $X$ is {\it dense-$\mathcal{P}$} if each dense subset of $X$ has the property $\mathcal{P}$. In this paper, we mainly discuss dense subsets of a space $X$,…

Let $G$ be a (non compact) connected simply connected locally compact second countable Lie group, either abelian or unimodular of type I, and $\rho$ an irreducible unitary representation of $G$. Then, we define the analytic torsion of $G$…

The main objects of study in this article are pairs $(G, \mathcal{H})$ where $G$ is a topological group with a compact open subgroup, and $\mathcal{H}$ is a finite collection of open subgroups. We develop geometric techniques to study the…