The coarse Baum–Connes conjecture for Busemann nonpositively curved spaces

Abstract

We prove that the coarse assembly maps for proper metric spaces that are nonpositively curved in the sense of Busemann are isomorphisms, where we do not assume that the spaces have bounded coarse geometry. Also it is shown that we can calculate the coarse $K$-homology and the $K$-theory of the Roe algebra by using the visual boundaries.