Atiyah covering index theorem for riemannian foliations

Moulay-Tahar Benameur; James L. Heitsch

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arXiv · 1804.07033

Atiyah covering index theorem for riemannian foliations

Moulay-Tahar Benameur·James L. Heitsch

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Abstract

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.

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BibTeX RIS

Moulay-Tahar Benameur, James L. Heitsch. 2018-04-19. Atiyah covering index theorem for riemannian foliations. https://arxiv.org/abs/1804.07033

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