Coarse geometry of Hecke pairs and K-theory
Clément Dell'Aiera (École normale supérieure de Lyon)
Thursday 12th May 16:00-17:00 Maths 311B
Defined by Shimura in the 50s, Hecke pairs are almost normal inclusions of subgroups. Originally number theoretic objects, they were introduced to operator algebraists by the celebrated work of Bost and Connes when they discovered a C*-dynamical system whose partition function was the zêta function. To a Hecke pair, one can associate a locally compact totally disconnected group replacing the quotient, its so called Schlichting completion.
We give a geometric interpretation to Hecke pairs, and, with the help of the Schlichting completion, study the K-theory of the reduced group algebra of a group with an almost normal subgroup. This allows to prove new stability results for the Baum-Connes and Novikov conjectures, as well as establishing new examples of groups satisfying the Baum-Connes conjecture with coefficients.