An equivariant Poincaré duality for proper cocompact actions by matrix groups (Q2697950)

Summary: Let \(G\) be a linear Lie group acting properly on a \(G\)-\(\mathrm{spin}^c\) manifold \(M\) with compact quotient. We give a short proof 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.