  We propose to use the winding number of the gradient of a scalar potential as
a simple topological index that relates critical points in the interior of the
scalar field space to the behavior of the potential at the (asymptotic)
boundary of the field space. We demonstrate this technique for supersymmetric
flux compactifications of M-theory on Calabi-Yau four-folds, and use the Fermat
sextic as a simple, one-parameter example.
