Index theory for basic Dirac operators on Riemannian foliations
Differential Geometry
2021-01-28 v1
Abstract
In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.
Cite
@article{arxiv.1008.1757,
title = {Index theory for basic Dirac operators on Riemannian foliations},
author = {Jochen Brüning and Franz W. Kamber and Ken Richardson},
journal= {arXiv preprint arXiv:1008.1757},
year = {2021}
}
Comments
33 pages