Le séminaire du lundi d'algèbre de Saint-Etienne

Sara AZZALI : "K-théorie algébrique"

Le séminaire du Lundi d'Algèbre de Saint-Étienne. Il aura lieu environ toutes les semaines à 15h45 dans la salle de séminaire

Lundi 3 avril 2017

Orateur : Sara AZZALI (Université de Postdam)

Titre : Flat bundles and K-theory with R/Z-coefficients

Résumé :
Let G be the fundamental group of a closed manifold X and  \alpha: G —> U(n) a finite dimensional unitary representation, i.e. a flat unitary vector bundle over X.
To these data, one can associate a class [\alpha] in the (topological) K-theory group with R/Z-coefficients.

In this talk, after introducing the needed tools, we describe the construction of the class and discuss its role of secondary invariant.
By means of an operator algebraic point of view, the class [\alpha] can be generalised it to the noncommutative setting of a discrete group G suitably acting on a C^*-algebra A.

Based on joint work with Paolo Antonini and Georges Skandalis.