A Hopf Index Theorem for foliations
Differential Geometry
2021-01-28 v1 Spectral Theory
Abstract
We formulate and prove an analog of the Hopf Index Theorem for Riemannian foliations. We compute the basic Euler characteristic of a closed Riemannian manifold as a sum of indices of a non-degenerate basic vector field at critical leaf closures. The primary tool used to establish this result is an adaptation to foliations of the Witten deformation method.
Keywords
Cite
@article{arxiv.math/0104128,
title = {A Hopf Index Theorem for foliations},
author = {Victor Belfi and Efton Park and Ken Richardson},
journal= {arXiv preprint arXiv:math/0104128},
year = {2021}
}
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26 pages