  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.

Differential Geometry;Spectral Theory