Universidad de Buenos Aires Expositor: Markus Land (Copenhagen) Título: Paschke duality and assembly maps. Martes 21 de setiembre, 10 AM, Argentina time (UTC-3).
Resumen: I will report on joint work with U. Bunke and A. Engel. I will focus on the goal of identifying different constructions of assembly maps appearing in the Baum—Connes conjecture, most notably Kasparov’s analytical assembly map and the homotopy theoretic assembly map building on work of Davis—Lück. I will explain what the main differences between these assembly maps are, indicate the state-of-the-art and indicate what our approach for a comparison is. As a main step of a comparison, we prove an equivariant form of Paschke duality which might be of independent interest and which I will indicate as well. Finally, I will indicate that, as a byproduct of our comparison result, we obtain a different proof of a (special case of a) result of Chabert—Echterhoff, which states that the Kasparov assembly map is an isomorphism for compactly induced coefficients (we treat only the case of discrete groups throughout).
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