On the quasidiagonality of Roe algebras.

Let X be a noncompact discrete metric space with bounded geometry. Associated with X are two C*-algebras, the so-called uniform Roe algebra B*( X) and coarse Roe algebra C*( X), which arose from the index theory on noncompact complete Riemannian manifolds. In this paper, we describe the quasidiagonality of B*( X) and C*( X) in terms of coarse geometric invariants. Some necessary and sufficient conditions are given, which involve the Fredholm index and coarse connectedness of metric spaces. [ABSTRACT FROM AUTHOR]