Weak amenability and C*-exactness for infinitely presented small cancellation groups
Weak amenability and C*-exactness for infinitely presented small cancellation groups
Let be a finitely generated group defined by an infinite presentation satisfying the small cancellation condition . Weak amenability and -exactness (equivalently, Guoliang Yu's property A) should hold for . Small cancellation approximation conjecture. Every such group is weakly amenable and -exact. This would extend the known Metric Approximation Property for the reduced -algebra and Fourier algebra of these groups to stronger approximation properties; the source postpones further considerations to future work.
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Primary source
Goulnara Arzhantseva and Cornelia Drutu, “Geometry of infinitely presented small cancellation groups, Rapid Decay and quasi-homomorphisms”, arXiv:1212.5280 (2012).
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