Singularities of projected immersions revisited

TL;DR

This paper revisits Szucs's 2000 result on the cobordism of r-tuple-point manifolds and their projections, providing an explicit bordism construction that enhances understanding of the geometric relationships involved.

Contribution

It extends Szucs's theorem by explicitly constructing the bordism between the natural mappings of the manifolds involved.

Findings

Explicit bordism construction between manifolds

Extension of Szucs's cobordism result

Enhanced understanding of projection singularities

Abstract

Sz\H ucs proved in 2000 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 slightly 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 the bordism explicitly.