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• W3181200570 abstract "We construct a natural transformation between two versions of $G$-equivariant $K$-homology with coefficients in a $G$-$C^{*}$-category for a countable discrete group $G$. Its domain is a coarse geometric $K$-homology and its target is the usual analytic $K$-homology. Following classical terminology, we call this transformation the Paschke transformation. We show that under certain finiteness assumptions on a $G$-space $X$, the Paschke transformation is an equivalence on $X$. As an application, we provide a direct comparison of the homotopy theoretic Davis-Luck assembly map with Kasparov's analytic assembly map appearing in the Baum-Connes conjecture." @default.
• W3181200570 created "2021-07-19" @default.
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• W3181200570 date "2021-07-06" @default.
• W3181200570 modified "2023-09-27" @default.
• W3181200570 title "Paschke duality and assembly maps" @default.
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