A Hopf Index Theorem for foliations

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.

26 pages

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