Boundary of free products of metric spaces

Abstract

In this paper, we compute (co)homologies of ideal boundaries of free products of geodesic coarsely convex spaces in terms of those of each of the components. The (co)homology theories we consider are, $K$-theory, Alexander-Spanier cohomology, $K$-homology, and Steenrod homology. These computations led to the computation of $K$-theory of the Roe algebra of free products of geodesic coarsely convex spaces via the coarse Baum-Connes conjecture.

32 pages, 3 figures