On the quasidiagonality of Roe algebras

Abstract

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.