Property A and nuclearity of Roe algebras (application/pdf Object)

propAnuclear.pdf (application/pdf Object)

By Brodzki, Niblo and Wright. One knows that for a discrete group G, property A is equivalent to exactness/nuclearity of its translation algebra. But the same thing is not known for a general (uniformly discrete) coarse space. In this paper is a measure of the 'grouplikeness' of a coarse space in terms of "partial translation structures". If X is uniformly embeddable in a discrete group, then it has a "free partial translation structure" and the expected equivalence holds.

Comments: Gromov's counterexample construction gives a way of building an 'almost' injective embedding of a more-or-less arbitrary coarse space into a discrete group. Relate that to this paper!