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 $G$-spin${}^c$ 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.

13 pages

References in corpus (1)

• Geometric quantization and families of inner products