C*-académie

The Bost conjecture
Walther Paravicini (Muenster)
Friday 13 March 2009 15:00 -  Orléans -  Salle de Séminaire

Résumé :
The Bost conjecture is the little sister of the renowned conjecture of Baum and Connes. Instead of computing the K-theory of the reduced C*-algebra of a group G, the Bost conjecture asserts an isomorphism of the K-theory of the L^1-algebra of G and the G-equivariant K-homology of underline{E}G. The conjecture has been proved by V. Lafforgue in many important cases. We discuss what is known about permanence properties of the Bost conjecture, in particular we will consider the passage to subgroups and to direct limits. The main tool for the proof that the Bost conjecture passes to open subgroups uses constructions for groupoids which I am going to present in some detail. If time permits, we will discuss how one could possibly generalise the Bost conjecture to allow for Banach algebra coefficients (so far, there is only an evident conjecture with C*-coefficients) which would be the first step for a proof of the passage of the Bost conjecture to direct products.

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