DUALITY AND THE POINCARE-HOPF INEQUALITIES

摘要

In this article we obtain a duality result for an n-manifold N with boundary dN = N+UN a disjoint union, where N+ and N~ are arbitrarily chosen parts in dN and need not be compact. This duality result is used to generalize the Poincare-Hopf inequalities in a non-compact setting.