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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 is an observation that the proof of the same property for free groups due to Haagerup transfers directly to this more general situation. Examples of groups satisfying the hypotheses include free groups, surface groups, finitely generated Coxeter groups, right angled Artin groups and many small cancellation groups.
This is a survey of methods of proving or disproving the Rapid Decay property in groups. We present a centroid property of group actions on metric spaces. That property is a generalized (and corrected) version of the property (**)-relative hyperbolic
We study the geometry of infinitely presented groups satisfying the small cancelation condition C(1/8), and define a standard decomposition (called the criss-cross decomposition) for the elements of such groups. We use it to prove the Rapid Decay pro
We prove that the alternating group of a topologically free action of a countably infinite group $Gamma$ on the Cantor set has the property that all of its $ell^2$-Betti numbers vanish and, in the case that $Gamma$ is amenable, is stable in the sense
The chain group $C(G)$ of a locally compact group $G$ has one generator $g_{rho}$ for each irreducible unitary $G$-representation $rho$, a relation $g_{rho}=g_{rho}g_{rho}$ whenever $rho$ is weakly contained in $rhootimes rho$, and $g_{rho^*}=g_{rho}
We study the relation (and differences) between stability and Property (S) in the simple and stably finite framework. This leads us to characterize stable elements in terms of its support, and study these concepts from different sides : hereditary su