An equivariant Poincar\'e duality for proper cocompact actions by matrix groups

DOI10.4171/JNCG/468arXiv2009.13695MaRDI QIDQ6350093

Author name not available (Why is that?), Varghese Mathai

Publication date: 28 September 2020

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 Poincar'e 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.

Mathematics Subject Classification ID

Spin and Spin({}^c) geometry (53C27) Ext and (K)-homology (19K33) Equivariant (K)-theory (19L47)

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