Uniform K-theory, and Poincare duality for uniform K-homology

Abstract

We revisit Spakula's uniform K-homology, construct the external product for it and use this to deduce homotopy invariance of uniform K-homology. We define uniform K-theory and on manifolds of bounded geometry we give an interpretation of it via vector bundles of bounded geometry. We further construct a cap product with uniform K-homology and prove Poincare duality between uniform K-theory and uniform K-homology on spin-c manifolds of bounded geometry.