O grau de uma aplicação: uma abordagem via aplicação diferencial

Abstract

In this work, we study the concepts of degree and local degree for maps between manifolds. Furthermore, we define the Poincaré-Hopf index and study some relevant proprieties of this index such as the famous Poincaré-Hopf Theorem. In the sequence, we prove this theorem in the case of manifolds and we present a brief study about some generalizations of this important theorem in the case of bordered manifolds and singular varieties.