Spectrum-valued $\mathrm{KK}^G$, Paschke duality and assembly maps

Abstract: I will explain a version of Paschke-duality which connects the usual equivariant analytic $\mathrm{K}$-homology theory with the equivariant $\mathrm{K}$-homology theory derived from equivariant coarse $\mathrm{K}$-homology. The Davis-Lück assembly map can be expressed through the coarse homology theory. Using Paschke duality we identify it with the classical version of the Baum-Connes assembly map via descent and Kasparov’s projection. All this will be phrased using a spectrum-valued $\mathrm{KK}^G$-theory, and we allow coefficients in $\mathrm{C}^\ast$-categories with $G$-action.

algebraic topologydifferential geometrygeometric topologyK-theory and homology

Audience: researchers in the topic

Göttingen topology and geometry seminar

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