An equivariant Poincaré duality for proper cocompact actions by matrix groups

Abstract

Let G be a linear Lie group acting properly and isometrically on a G-spinc manifold M with compact quotient. We show that Poincaré duality holds between G-equivariant K-theory of M, defined using finite-dimensional G-vector bundles, and G-equivariant K-homology of M, defined through the geometric model of Baum and Douglas.