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

Paolo Antonini  (SISSA Trieste, Italy)

15:00-16:00, May 26, 2020


For a discrete group $\Gamma$ we construct a Baum-Connes map localised at the group unit element. 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. A second interesting feature of the localised assembly map is functoriality 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 KK_{\R}-theory of the classifying space for free and proper actions E\Gamma with the classifying space for proper actions \underline{E}\Gamma. Based on joint work with Sara Azzali and Georges Skandalis.

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