Atiyah covering index theorem for riemannian foliations
Geometric Topology
2018-04-20 v1 Differential Geometry
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 covering index theorem.
Keywords
Cite
@article{arxiv.1804.07033,
title = {Atiyah covering index theorem for riemannian foliations},
author = {Moulay-Tahar Benameur and James L. Heitsch},
journal= {arXiv preprint arXiv:1804.07033},
year = {2018}
}