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arXiv · 1008.1757

Index theory for basic Dirac operators on Riemannian foliations

Jochen Brüning·Franz W. Kamber·Ken Richardson
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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.

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Jochen Brüning, Franz W. Kamber, Ken Richardson. 2010-08-10. Index theory for basic Dirac operators on Riemannian foliations. https://doi.org/10.1090/conm%2F546

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