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Large scale properties of groups; growth functions; Dehn functions; small cancellation properties; hyperbolicity and CAT(0); actions and representations; combinatorial group theory; presentations

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Characterization of exact groups via the existence of amenable actions on unital C*-algebras...

The answer to the question is positive: see Remark 6.6 in the paper https://arxiv.org/pdf/1904.06771.pdf The approximation property implies amenability in the sense of Claire Anantharaman Delaroche, t …
Alcides Buss's user avatar