The Baum–Connes conjecture localised at the unit element of a discrete group

Abstract: Let Γ be a discrete group; we construct a Baum–Connes map localised at the unit element of Γ. This is an assembly map in KK–theory with real coefficients leading to a form of the Baum–Connes conjecture which is intermediate between the Baum–Connes conjecture and the Strong Novikov conjecture. The localised assembly map has an interesting property: it is functorial with respect to group morphisms. We explain the construction and we show that the relation with the Novikov conjecture follows from a comparison at the level of KKR-theory of the classifying space for free and proper actions EΓ with the classifying space for proper actions EΓ. Based on joint work with Sara Azzali and Georges Skandalis.

algebraic topologydifferential geometrygeometric topologyK-theory and homology

Audience: researchers in the topic

Göttingen topology and geometry seminar

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