Sphere stratifications and the Gauss map

Source abstract

Synopsis There is a residual subset of embeddings of an m -manifold, M in R m+1 (m ≦ 6), for which the induced Maxwell subset on the sphere S m is a stratified subset. We define and study two different stratifications of this subset and their extensions to the whole S m : the Gauss stratification and the core stratification. We also find relations between the Euler numbers of the strata of the core stratification and the “exposed” singularities of the Gauss map on M .