Constructing generic smooth maps of a manifold into a surface with prescribed singular loci
Osamu Saeki · Annales de l’institut Fourier · 1995
It is known that the singular set S ( f ) of a generic smooth map f : M → N of an n -dimensional manifold into a surface is a closed 1-dimensional submanifold of M and that it has a natural stratification induced by the absolute index. In this paper, we give a complete characterization of those 1-dimensional (stratified) submanifolds which arise as the singular set of a generic map in terms of the homology class they represent.