Arbre de Noël du GDR "Géométrie non-commutative"

The Godbillon-Vey Invariant in KK-theory with Real Coefficients

2 déc. 2022, 11:30

1h

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Orateur

Prof. Sarah AZZALI (Università di Bari)

Description

The Godbillon-Vey invariant is a 3-degree cohomology class associated with a foliation of codimension 1 of a closed manifold M.
This classical invariant has been shown to be closely related to measure theory and dynamics of the foliation. It also plays a crucial role in index theory, as proved by Alain Connes.
We construct a natural class in bivariant $KK$-theory with real coefficients representing the Godbillon-Vey invariant. We shall explain these construction, see how the Godbillon-Vey invariant deals with a (densely defined) infinite trace, and the relation to the index theorem for measured foliations.
This is joint work with Paolo Antonini (Unisalento) and Georges Skandalis (Université Paris Cité).