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A Hopf Index Theorem for foliations

Victor Belfi·Efton Park·Ken Richardson
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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.

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Victor Belfi, Efton Park, Ken Richardson. 2001-04-11. A Hopf Index Theorem for foliations. https://doi.org/10.1016/s0926-2245(02)00165-1

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