Related papers: The Rapid Decay property and centroids in groups

We explain some simple methods to establish the property of Rapid Decay for a number of groups arising geometrically. We also give new examples of groups with the property of Rapid Decay. In particular we establish the property of Rapid…

These are the notes for the mini-course on the property of rapid decay given at the Erwin Schr\"odinger Institute in Vienna between March 14th and 18th, 2016, as a part of the Measured Group Theory program. They include parts which were…

We provide a new, dynamical criterion for the radial rapid decay property. We work out in detail the special case of the group $\Gamma := \mathbf{SL}_2(A)$, where $A := \mathbb{F}_q[X,X^{-1}]$ is the ring of Laurent polynomials with…

We study a notion of a Lipschitz, permutation-invariant "centroid" for triples of points in mapping class groups MCG(S), which satisfies a certain polynomial growth bound. A consequence (via work of Drutu-Sapir or Chatterji-Ruane) is the…

This work concerns a generalization of property (RD) from discrete groups to twisted \'etale groupoids equipped with a length function. We show that, under the assumption that the \'etale groupoid is principal, twisted property (RD) is…

Let Gamma be a discrete group satisfying the rapid decay property with respect to a length function which is conditionally negative. Then the reduced C*-algebra of Gamma has the metric approximation property. The central point of our proof…

We prove that the rapid decay property (RD) of groups is preserved by graph products defined on finite simplicial graphs.

We introduce a notion of the Rapid Decay Property (RDP) for Fell bundles over locally compact Hausdorff \'etale groupoids, extending earlier rapid decay theories for \'etale groupoids and twists. Our approach yields analytic control on…

We prove that a finitely generated group $G$ hyperbolic relative to the collection of finitely generated subgroups H_1,..., H_m has the Rapid Decay property if and only if each H_i, i=1,2,..., m, has the Rapid Decay property.

The fundamental group of a closed irreducible 3-dimensional manifold has the Rapid Decay property if and only if it is not virtually Sol. This is proved by studying distortion of length functions in graphs of groups, and the stability of…

We introduce the Property of Rapid Decay for discrete quantum groups by equivalent characterizations that generalize the classical ones. We then investigate examples, proving in particular the Property of Rapid Decay for unimodular free…

We generalize the notion of rapid decay property for a group $G$ to pairs of groups $(G,H)$ where $H$ is a finitely generated subgroup of $G$, where typically the subgroup $H$ does not have rapid decay. We deduce some isomorphisms in…

For a locally compact group, property RD gives a control on the convolution norm of any compactly supported measure in terms of the $L^2$-norm of its density and the diameter of its support. We give a complete classification of those Lie…

We consider bicrossed products obtained by twisting compact semi-direct products by a suitable finite subgroup. Under some restriction, we give a practical criterion for the discrete dual of such bicrossed products to have the rapid decay…

We work in the density model of random groups. We prove that they satisfy an isoperimetric inequality with sharp constant $1-2d$ depending upon the density parameter $d$. This implies in particular a property generalizing the ordinary $C'$…

We establish property $R_\infty$ for Artin groups of spherical type $D_n$, $n\ge6$, their central quotients, and also for large hyperbolic-type free-of-infinity Artin groups and some other classes of large-type Artin groups. The key…

We show that the reduced groupoid C*-algebras of continuous fields of \'etale groupoids satisfying the rapid decay property yield continuous fields of C*-algebras. This establishes a new sufficient criterion that applies in the non-amenable…

We study \emph{property RD} in terms of rapid decay of matrix coefficients. We give new formulations of property RD in terms of a $L^{1}$-integra\-bility condition of a Banach representation. Combining this new definition with the existence…

This is an introduction to the Rapid Decay property, with a survey of known results and equivalent definitions of this property. We also discuss in details the easy case when G = Z. Everything in this paper is well-known by different sets…

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…