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Exactness and uniform embeddability of discrete groups, written with J. Kaminker

This paper appeared in the Journal of the London Math. Society., 70 (2004), 703-718.

Abstract

We define a numerical quasi-isometry invariant R(G), of a finitely generated group G, whose values parametrize the difference between G being uniformly embeddable in a Hilbert space and its reduced C*-algebra being exact. As an application we show that if a finitely generated group G admits a uniform embedding into Hilbert space H for which the image of G, in the metric induced from H, is a quasi-geodesic space then the reduced C*-algebra of G is exact.