Resumen de Construction of Smooth Sphere Maps with Given Degree and a Generalization of Morse Index Formula for Smooth Vector Fields
This paper presents a fundamental lemma concerning the index of a zero of a vector field. Based on this lemma one obtains a procedure of constructing a higher dimensional smooth sphere map from a lower dimensional one and gives an explicit formula for smooth sphere map with a given topological degree. Also based on this lemma, a new proof of the generalized Morse index formula is presented for smooth vector fields on a manifold with boundary.
