Atiyah covering index theorem for Riemannian foliations

Benameur, Moulay-Tahar; Heitsch, James

doi:10.1090/tran/7731

Atiyah covering index theorem for Riemannian foliations
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by Moulay-Tahar Benameur and James L. Heitsch PDF

Trans. Amer. Math. Soc. 371 (2019), 5875-5897 Request permission

Abstract:

We use the symbol calculus for foliations developed by the authors in 2017 to derive a cohomological formula for the Connes–Chern character of the Type II spectral triple given also by the authors in 2018. 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.

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