This concept generalizes the usual index of the non-degenerated isolated zero of the smooth tangent vector field. On the basis of this concept we prove an equivariant analog of the classical Poincare-Hopf theorem. As an application of the main result we deduce an exact addition formula for the first-half integer Pontryagin class in complex cobordism. We denote the connected component of the zero set of s as M 1 . We assume that there is a vector field s, tangent to E along the fibre.
E is an inclusion.