Operator algebras conference in memory of Étienne Blanchard

Inverting the assembly map (after S. Nishikawa)

10 avr. 2019, 09:00

50m

Bâtiment Sophie Germain, Amphi Turing (Université Paris Diderot)

Abstract

Orateur

Alain Valette (Univ. Neuchatel)

Description

In a recent preprint (https://arxiv.org/abs/1808.08298), Nishikawa introduces a property $(\gamma )$ for elements $x$ in the Kasparov ring $R(G)$: it says that the Fredholm module defining $x$ carries a compatible action of $C_0(X)$, where $X$ is a $G$-compact model for the classifying space for proper actions of $G$. The basic observation is that $x$ then defines a morphism $\text{Undefined control sequence C}$, that is a candidate for a right inverse for the Baum-Connes assembly map. It is proved that, if $x=1$ in $R(G)$, it is indeed the case. Using this, new proofs of the Baum-Connes conjecture with coefficients are obtained for Euclidean motion groups, and for groups acting properly co-compactly on locally finite trees.