arXiv subjects
Publications and source records attributed to Graham Niblo.
In this note we study the natural question of when the generalised F{\o}lner sets exhibiting property A can be chosen to be subsets of the space itself. We show that for many property A spaces $X$, this is indeed possible. Specifically this holds: for all discrete bounded geometry metric spaces which coarsely have all components unbounded; for all countable discrete groups; and for all box spaces.
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.
We combine ideas of Scott and Swarup on good position for almost invariant subsets of a group with ideas of Sageev on constructing cubings from such sets. We construct cubings which are more canonical than in Sageev's original construction. We also show that almost invariant sets can be chosen to be in very good position.