Atiyah covering index theorem for riemannian foliations

Moulay-Tahar Benameur (1) , James L. Heitsch (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Mathematics, Statistics, and Computer Science

We use the symbol calculus for foliations developed in our previous paper to derive a cohomological formula for the Connes-Chern character of the semi-finite spectral triple. The same proof works for the Type I spectral triple of Connes-Moscovici. The cohomology classes of the two Connes-Chern characters induce the same map on the image of the maximal Baum-Connes map in K-theory, thereby proving an Atiyah $L^2$ covering index theorem.

Domaines: Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]

Moulay-Tahar Benameur, James L. Heitsch. Atiyah covering index theorem for riemannian foliations. Transactions of the American Mathematical Society, In press, ⟨10.1090/tran/7731⟩. ⟨hal-01819115⟩