Singularities of projected immersions revisited

Abstract

Szűcs proved [Bull. London Math. Soc. 32 (2000) 364-374] that the $r$–tuple-point manifold of a generic immersion is cobordant to the ${\Sigma }^{1_{r-1}}$–point manifold of its generic projection. Here we extend this by showing that the natural mappings of these manifolds are bordant to each other. The main novelty of our approach is that we construct an explicit geometric realization of the bordism.