AG Lie-Gruppen: Clément Dell'Aiera

Vortragender: Clément Dell’Aiera, Department of Mathematics, ENS Lyon
Veranstalter: Kang Li

Titel: Coarse geometry of Hecke pairs and K-theory

Abstract:
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.